How can I make a Region equal to another in JavaFX?

You have to set the size of the ´Region´. Try modifying your method to:

private final double width = 50;
private final double height = 50;

private static Region createRegionIcon(String svgData, String color) {
    SVGPath icon = new SVGPath();
    icon.setContent(svgData);
    
    Region svgRegion = new Region();
    svgRegion.setShape(icon);

    svgRegion.setMinSize(width, height);
    svgRegion.setPrefSize(width, height);
    svgRegion.setMaxSize(width, height);

    svgRegion.setStyle("-fx-background-color: " + color);

    return svgRegion;
}

Working example:

import javafx.application.Application;
import javafx.geometry.Pos;
import javafx.scene.Scene;
import javafx.scene.layout.HBox;
import javafx.scene.layout.Region;
import javafx.scene.shape.SVGPath;
import javafx.stage.Stage;

public class App extends Application {

    private static final double WIDTH = 50;
    private static final double HEIGHT = 50;

    private final String svgData1 = "M55,27.5C55,12.337,42.663,0,27.5,0S0,12.337,0,27.5c0,8.009,3.444,15.228,8.926,20.258l-0.026,0.023l0.892,0.752c0.058,0.049,0.121,0.089,0.179,0.137c0.474,0.393,0.965,0.766,1.465,1.127c0.162,0.117,0.324,0.234,0.489,0.348c0.534,0.368,1.082,0.717,1.642,1.048c0.122,0.072,0.245,0.142,0.368,0.212c0.613,0.349,1.239,0.678,1.88,0.98c0.047,0.022,0.095,0.042,0.142,0.064c2.089,0.971,4.319,1.684,6.651,2.105c0.061,0.011,0.122,0.022,0.184,0.033c0.724,0.125,1.456,0.225,2.197,0.292c0.09,0.008,0.18,0.013,0.271,0.021C25.998,54.961,26.744,55,27.5,55c0.749,0,1.488-0.039,2.222-0.098c0.093-0.008,0.186-0.013,0.279-0.021c0.735-0.067,1.461-0.164,2.178-0.287c0.062-0.011,0.125-0.022,0.187-0.034c2.297-0.412,4.495-1.109,6.557-2.055c0.076-0.035,0.153-0.068,0.229-0.104c0.617-0.29,1.22-0.603,1.811-0.936c0.147-0.083,0.293-0.167,0.439-0.253c0.538-0.317,1.067-0.648,1.581-1c0.185-0.126,0.366-0.259,0.549-0.391c0.439-0.316,0.87-0.642,1.289-0.983c0.093-0.075,0.193-0.14,0.284-0.217l0.915-0.764l-0.027-0.023C51.523,42.802,55,35.55,55,27.5z M2,27.5C2,13.439,13.439,2,27.5,2S53,13.439,53,27.5c0,7.577-3.325,14.389-8.589,19.063c-0.294-0.203-0.59-0.385-0.893-0.537l-8.467-4.233c-0.76-0.38-1.232-1.144-1.232-1.993v-2.957c0.196-0.242,0.403-0.516,0.617-0.817c1.096-1.548,1.975-3.27,2.616-5.123c1.267-0.602,2.085-1.864,2.085-3.289v-3.545c0-0.867-0.318-1.708-0.887-2.369v-4.667c0.052-0.519,0.236-3.448-1.883-5.864C34.524,9.065,31.541,8,27.5,8s-7.024,1.065-8.867,3.168c-2.119,2.416-1.935,5.345-1.883,5.864v4.667c-0.568,0.661-0.887,1.502-0.887,2.369v3.545c0,1.101,0.494,2.128,1.34,2.821c0.81,3.173,2.477,5.575,3.093,6.389v2.894c0,0.816-0.445,1.566-1.162,1.958l-7.907,4.313c-0.252,0.137-0.502,0.297-0.752,0.476C5.276,41.792,2,35.022,2,27.5z M42.459,48.132c-0.35,0.254-0.706,0.5-1.067,0.735c-0.166,0.108-0.331,0.216-0.5,0.321c-0.472,0.292-0.952,0.57-1.442,0.83c-0.108,0.057-0.217,0.111-0.326,0.167c-1.126,0.577-2.291,1.073-3.488,1.476c-0.042,0.014-0.084,0.029-0.127,0.043c-0.627,0.208-1.262,0.393-1.904,0.552c-0.002,0-0.004,0.001-0.006,0.001c-0.648,0.16-1.304,0.293-1.964,0.402c-0.018,0.003-0.036,0.007-0.054,0.01c-0.621,0.101-1.247,0.174-1.875,0.229c-0.111,0.01-0.222,0.017-0.334,0.025C28.751,52.97,28.127,53,27.5,53c-0.634,0-1.266-0.031-1.895-0.078c-0.109-0.008-0.218-0.015-0.326-0.025c-0.634-0.056-1.265-0.131-1.89-0.233c-0.028-0.005-0.056-0.01-0.084-0.015c-1.322-0.221-2.623-0.546-3.89-0.971c-0.039-0.013-0.079-0.027-0.118-0.04c-0.629-0.214-1.251-0.451-1.862-0.713c-0.004-0.002-0.009-0.004-0.013-0.006c-0.578-0.249-1.145-0.525-1.705-0.816c-0.073-0.038-0.147-0.074-0.219-0.113c-0.511-0.273-1.011-0.568-1.504-0.876c-0.146-0.092-0.291-0.185-0.435-0.279c-0.454-0.297-0.902-0.606-1.338-0.933c-0.045-0.034-0.088-0.07-0.133-0.104c0.032-0.018,0.064-0.036,0.096-0.054l7.907-4.313c1.36-0.742,2.205-2.165,2.205-3.714l-0.001-3.602l-0.23-0.278c-0.022-0.025-2.184-2.655-3.001-6.216l-0.091-0.396l-0.341-0.221c-0.481-0.311-0.769-0.831-0.769-1.392v-3.545c0-0.465,0.197-0.898,0.557-1.223l0.33-0.298v-5.57l-0.009-0.131c-0.003-0.024-0.298-2.429,1.396-4.36C21.583,10.837,24.061,10,27.5,10c3.426,0,5.896,0.83,7.346,2.466c1.692,1.911,1.415,4.361,1.413,4.381l-0.009,5.701l0.33,0.298c0.359,0.324,0.557,0.758,0.557,1.223v3.545c0,0.713-0.485,1.36-1.181,1.575l-0.497,0.153l-0.16,0.495c-0.59,1.833-1.43,3.526-2.496,5.032c-0.262,0.37-0.517,0.698-0.736,0.949l-0.248,0.283V39.8c0,1.612,0.896,3.062,2.338,3.782l8.467,4.233c0.054,0.027,0.107,0.055,0.16,0.083C42.677,47.979,42.567,48.054,42.459,48.132z";
    private final String svgData2 = "m435.710938 117.226562-6.925782-4 12-20.796874 6.925782 4 12-20.800782c3.1875-5.515625 4.050781-12.074218 2.398437-18.226562-1.648437-6.152344-5.679687-11.394532-11.199219-14.574219l-13.863281-8c-5.515625-3.1875-12.070313-4.050781-18.222656-2.398437-6.152344 1.652343-11.394531 5.679687-14.578125 11.199218l-12 20.800782 6.929687 4-12 20.796874-6.929687-4-12.246094 21.28125v-106.296874h-320c-26.5.027343-47.9726562 21.503906-48 48v352c.0273438 26.5 21.5 47.972656 48 48h320v-213.703126l59.710938-103.421874 13.855468 8-24 41.597656 13.859375 8 32-55.421875zm-6.640626-68.503906 13.859376 8c1.835937 1.0625 3.179687 2.8125 3.730468 4.863282.546875 2.050781.257813 4.234374-.804687 6.074218l-4 6.929688-27.710938-16 4-6.929688c2.207031-3.828125 7.097657-5.144531 10.925781-2.9375zm-14.613281 28.519532 12.472657 7.203124-12 20.796876-13.859376-8 12-20.796876zm-366.457031-61.03125h304v24h-312v16h312v24h-304c-17.671875 0-32-14.324219-32-32 0-17.671876 14.328125-32 32-32zm304 416h-296v-296h-16v294.863281c-14.085938-3.636719-23.945312-16.316407-24-30.863281v-316.320313c6.738281 6.0625 15.0625 10.085937 24 11.601563v24.71875h16v-24h296v38.007812l-116.65625 202.058594-4.289062 71.429687 59.714843-39.429687 61.230469-106.058594zm-101.039062-89.09375 26.078124 15.054687-28.09375 18.542969zm34.894531 1.664062-6.925781-4 108-187.058594-13.859376-8-108 187.058594-3.460937-2-3.464844-2 128-221.695312 27.710938 16zm0 0";
    private final String svgData3 = "m72.808594 48h-64.960938c-4.332031.003906-7.84374975 3.515625-7.847656 7.847656v384.304688c.00390625 4.332031 3.515625 7.84375 7.847656 7.847656h288.3125c4.332032-.003906 7.84375-3.515625 7.847656-7.847656v-384.304688c-.003906-4.332031-3.515624-7.84375-7.847656-7.847656h-64.953125c-3.828125 18.613281-20.199219 31.976562-39.199219 32h-80c-19-.023438-35.371093-13.386719-39.199218-32zm215.199218 360h-272v-16h272zm0-32h-272v-16h272zm0-32h-272v-16h272zm0-32h-272v-16h272zm0-32h-272v-16h272zm-183.160156-175.960938c3.742188.394532 6.699219 3.34375 7.113282 7.082032l5.382812 48.4375 11.808594-19.679688c1.640625-2.726562 4.746094-4.222656 7.902344-3.804687s5.761718 2.664062 6.640624 5.726562l8.90625 31.136719 15.8125-47.464844c1.023438-3.074218 3.796876-5.230468 7.027344-5.460937 3.230469-.226563 6.28125 1.511719 7.726563 4.414062l13.785156 27.574219h91.054687v16h-96c-3.046874.015625-5.839843-1.699219-7.199218-4.425781l-7.359375-14.726563-17.890625 53.679688c-1.136719 3.304687-4.261719 5.511718-7.757813 5.472656-3.507812-.074219-6.558593-2.425781-7.519531-5.800781l-10.9375-38.269531-14.519531 24.191406c-1.769531 2.941406-5.214844 4.425781-8.566407 3.691406-3.351562-.730469-5.863281-3.523438-6.242187-6.933594l-4-35.789062-20.480469 61.4375c-1.050781 3.152344-3.9375 5.324218-7.253906 5.464844h-.273438c-3.199218 0-6.089843-1.90625-7.351562-4.847657l-21.921875-51.144531h-26.726563v-16h32c3.199219 0 6.089844 1.90625 7.351563 4.847656l15.710937 36.65625 25.34375-76c1.195313-3.5625 4.695313-5.832031 8.433594-5.464844zm0 0";

    @Override
    public void start(Stage stage) {
    
        Region svgShape1 = createRegionIcon(svgData1, "blue");
        Region svgShape2 = createRegionIcon(svgData2, "red");
        Region svgShape3 = createRegionIcon(svgData3, "green");
    
        HBox pane = new HBox();
    
        pane.setAlignment(Pos.CENTER);
        pane.setSpacing(10);
        pane.setStyle("-fx-background-color: white;");
    
        pane.getChildren().addAll(svgShape1, svgShape2, svgShape3);

        Scene scene = new Scene(pane);

        stage.setScene(scene);

        stage.show();

    }

    private static Region createRegionIcon(String svgData, String color) {
        SVGPath icon = new SVGPath();
        icon.setContent(svgData);
    
        Region svgRegion = new Region();
        svgRegion.setShape(icon);

        svgRegion.setMinSize(WIDTH, HEIGHT);
        svgRegion.setPrefSize(WIDTH, HEIGHT);
        svgRegion.setMaxSize(WIDTH, HEIGHT);

        svgRegion.setStyle("-fx-background-color: " + color);

        return svgRegion;
    }

    public static void main(String[] args) {
        launch();
    }

}

Output:

Regions can be shaped in CSS using the -fx-shape CSS property

Using this technique, the explicit creation of an SVGPath is not necessary.

See moderna.css in the JavaFX source for many examples of applying shapes to regions.

If you wanted two regions to have the same shape, you could do that by applying the same style class to different instances of Region.

The shaped regions can be colored by setting the -fx-background-color.

The shaped regions won't be seen unless they have a non-zero size. The region size can be managed via min/max/pref height/width settings (either in java code, FXML, or CSS). These settings provide instructions to the layout pane enclosing the region on how to size that region.

Here is an example of using -fx-shape to shape regions. The code is based on that in Oboe's answer, just adapted to use an external style sheet and slightly different coloring.

region-styling.css

.layout-pane {
    -fx-spacing: 10;
    -fx-background-color: white;
}

.icon {
    -fx-min-width: 50;
    -fx-pref-width: 50;
    -fx-max-width: 50;

    -fx-min-height: 50;
    -fx-pref-height: 50;
    -fx-max-height: 50;
}

.user-icon {
    -fx-shape: "M55,27.5C55,12.337,42.663,0,27.5,0S0,12.337,0,27.5c0,8.009,3.444,15.228,8.926,20.258l-0.026,0.023l0.892,0.752c0.058,0.049,0.121,0.089,0.179,0.137c0.474,0.393,0.965,0.766,1.465,1.127c0.162,0.117,0.324,0.234,0.489,0.348c0.534,0.368,1.082,0.717,1.642,1.048c0.122,0.072,0.245,0.142,0.368,0.212c0.613,0.349,1.239,0.678,1.88,0.98c0.047,0.022,0.095,0.042,0.142,0.064c2.089,0.971,4.319,1.684,6.651,2.105c0.061,0.011,0.122,0.022,0.184,0.033c0.724,0.125,1.456,0.225,2.197,0.292c0.09,0.008,0.18,0.013,0.271,0.021C25.998,54.961,26.744,55,27.5,55c0.749,0,1.488-0.039,2.222-0.098c0.093-0.008,0.186-0.013,0.279-0.021c0.735-0.067,1.461-0.164,2.178-0.287c0.062-0.011,0.125-0.022,0.187-0.034c2.297-0.412,4.495-1.109,6.557-2.055c0.076-0.035,0.153-0.068,0.229-0.104c0.617-0.29,1.22-0.603,1.811-0.936c0.147-0.083,0.293-0.167,0.439-0.253c0.538-0.317,1.067-0.648,1.581-1c0.185-0.126,0.366-0.259,0.549-0.391c0.439-0.316,0.87-0.642,1.289-0.983c0.093-0.075,0.193-0.14,0.284-0.217l0.915-0.764l-0.027-0.023C51.523,42.802,55,35.55,55,27.5z M2,27.5C2,13.439,13.439,2,27.5,2S53,13.439,53,27.5c0,7.577-3.325,14.389-8.589,19.063c-0.294-0.203-0.59-0.385-0.893-0.537l-8.467-4.233c-0.76-0.38-1.232-1.144-1.232-1.993v-2.957c0.196-0.242,0.403-0.516,0.617-0.817c1.096-1.548,1.975-3.27,2.616-5.123c1.267-0.602,2.085-1.864,2.085-3.289v-3.545c0-0.867-0.318-1.708-0.887-2.369v-4.667c0.052-0.519,0.236-3.448-1.883-5.864C34.524,9.065,31.541,8,27.5,8s-7.024,1.065-8.867,3.168c-2.119,2.416-1.935,5.345-1.883,5.864v4.667c-0.568,0.661-0.887,1.502-0.887,2.369v3.545c0,1.101,0.494,2.128,1.34,2.821c0.81,3.173,2.477,5.575,3.093,6.389v2.894c0,0.816-0.445,1.566-1.162,1.958l-7.907,4.313c-0.252,0.137-0.502,0.297-0.752,0.476C5.276,41.792,2,35.022,2,27.5z M42.459,48.132c-0.35,0.254-0.706,0.5-1.067,0.735c-0.166,0.108-0.331,0.216-0.5,0.321c-0.472,0.292-0.952,0.57-1.442,0.83c-0.108,0.057-0.217,0.111-0.326,0.167c-1.126,0.577-2.291,1.073-3.488,1.476c-0.042,0.014-0.084,0.029-0.127,0.043c-0.627,0.208-1.262,0.393-1.904,0.552c-0.002,0-0.004,0.001-0.006,0.001c-0.648,0.16-1.304,0.293-1.964,0.402c-0.018,0.003-0.036,0.007-0.054,0.01c-0.621,0.101-1.247,0.174-1.875,0.229c-0.111,0.01-0.222,0.017-0.334,0.025C28.751,52.97,28.127,53,27.5,53c-0.634,0-1.266-0.031-1.895-0.078c-0.109-0.008-0.218-0.015-0.326-0.025c-0.634-0.056-1.265-0.131-1.89-0.233c-0.028-0.005-0.056-0.01-0.084-0.015c-1.322-0.221-2.623-0.546-3.89-0.971c-0.039-0.013-0.079-0.027-0.118-0.04c-0.629-0.214-1.251-0.451-1.862-0.713c-0.004-0.002-0.009-0.004-0.013-0.006c-0.578-0.249-1.145-0.525-1.705-0.816c-0.073-0.038-0.147-0.074-0.219-0.113c-0.511-0.273-1.011-0.568-1.504-0.876c-0.146-0.092-0.291-0.185-0.435-0.279c-0.454-0.297-0.902-0.606-1.338-0.933c-0.045-0.034-0.088-0.07-0.133-0.104c0.032-0.018,0.064-0.036,0.096-0.054l7.907-4.313c1.36-0.742,2.205-2.165,2.205-3.714l-0.001-3.602l-0.23-0.278c-0.022-0.025-2.184-2.655-3.001-6.216l-0.091-0.396l-0.341-0.221c-0.481-0.311-0.769-0.831-0.769-1.392v-3.545c0-0.465,0.197-0.898,0.557-1.223l0.33-0.298v-5.57l-0.009-0.131c-0.003-0.024-0.298-2.429,1.396-4.36C21.583,10.837,24.061,10,27.5,10c3.426,0,5.896,0.83,7.346,2.466c1.692,1.911,1.415,4.361,1.413,4.381l-0.009,5.701l0.33,0.298c0.359,0.324,0.557,0.758,0.557,1.223v3.545c0,0.713-0.485,1.36-1.181,1.575l-0.497,0.153l-0.16,0.495c-0.59,1.833-1.43,3.526-2.496,5.032c-0.262,0.37-0.517,0.698-0.736,0.949l-0.248,0.283V39.8c0,1.612,0.896,3.062,2.338,3.782l8.467,4.233c0.054,0.027,0.107,0.055,0.16,0.083C42.677,47.979,42.567,48.054,42.459,48.132z";
    -fx-background-color: blue;
}

.notepad-icon {
    -fx-shape: "m435.710938 117.226562-6.925782-4 12-20.796874 6.925782 4 12-20.800782c3.1875-5.515625 4.050781-12.074218 2.398437-18.226562-1.648437-6.152344-5.679687-11.394532-11.199219-14.574219l-13.863281-8c-5.515625-3.1875-12.070313-4.050781-18.222656-2.398437-6.152344 1.652343-11.394531 5.679687-14.578125 11.199218l-12 20.800782 6.929687 4-12 20.796874-6.929687-4-12.246094 21.28125v-106.296874h-320c-26.5.027343-47.9726562 21.503906-48 48v352c.0273438 26.5 21.5 47.972656 48 48h320v-213.703126l59.710938-103.421874 13.855468 8-24 41.597656 13.859375 8 32-55.421875zm-6.640626-68.503906 13.859376 8c1.835937 1.0625 3.179687 2.8125 3.730468 4.863282.546875 2.050781.257813 4.234374-.804687 6.074218l-4 6.929688-27.710938-16 4-6.929688c2.207031-3.828125 7.097657-5.144531 10.925781-2.9375zm-14.613281 28.519532 12.472657 7.203124-12 20.796876-13.859376-8 12-20.796876zm-366.457031-61.03125h304v24h-312v16h312v24h-304c-17.671875 0-32-14.324219-32-32 0-17.671876 14.328125-32 32-32zm304 416h-296v-296h-16v294.863281c-14.085938-3.636719-23.945312-16.316407-24-30.863281v-316.320313c6.738281 6.0625 15.0625 10.085937 24 11.601563v24.71875h16v-24h296v38.007812l-116.65625 202.058594-4.289062 71.429687 59.714843-39.429687 61.230469-106.058594zm-101.039062-89.09375 26.078124 15.054687-28.09375 18.542969zm34.894531 1.664062-6.925781-4 108-187.058594-13.859376-8-108 187.058594-3.460937-2-3.464844-2 128-221.695312 27.710938 16zm0 0";
    -fx-background-color: green;
}

.cardiac-arrest-icon {
    -fx-shape: "m72.808594 48h-64.960938c-4.332031.003906-7.84374975 3.515625-7.847656 7.847656v384.304688c.00390625 4.332031 3.515625 7.84375 7.847656 7.847656h288.3125c4.332032-.003906 7.84375-3.515625 7.847656-7.847656v-384.304688c-.003906-4.332031-3.515624-7.84375-7.847656-7.847656h-64.953125c-3.828125 18.613281-20.199219 31.976562-39.199219 32h-80c-19-.023438-35.371093-13.386719-39.199218-32zm215.199218 360h-272v-16h272zm0-32h-272v-16h272zm0-32h-272v-16h272zm0-32h-272v-16h272zm0-32h-272v-16h272zm-183.160156-175.960938c3.742188.394532 6.699219 3.34375 7.113282 7.082032l5.382812 48.4375 11.808594-19.679688c1.640625-2.726562 4.746094-4.222656 7.902344-3.804687s5.761718 2.664062 6.640624 5.726562l8.90625 31.136719 15.8125-47.464844c1.023438-3.074218 3.796876-5.230468 7.027344-5.460937 3.230469-.226563 6.28125 1.511719 7.726563 4.414062l13.785156 27.574219h91.054687v16h-96c-3.046874.015625-5.839843-1.699219-7.199218-4.425781l-7.359375-14.726563-17.890625 53.679688c-1.136719 3.304687-4.261719 5.511718-7.757813 5.472656-3.507812-.074219-6.558593-2.425781-7.519531-5.800781l-10.9375-38.269531-14.519531 24.191406c-1.769531 2.941406-5.214844 4.425781-8.566407 3.691406-3.351562-.730469-5.863281-3.523438-6.242187-6.933594l-4-35.789062-20.480469 61.4375c-1.050781 3.152344-3.9375 5.324218-7.253906 5.464844h-.273438c-3.199218 0-6.089843-1.90625-7.351562-4.847657l-21.921875-51.144531h-26.726563v-16h32c3.199219 0 6.089844 1.90625 7.351563 4.847656l15.710937 36.65625 25.34375-76c1.195313-3.5625 4.695313-5.832031 8.433594-5.464844zm0 0";
    -fx-background-color: red;
}

I set some items like height and width in the CSS.

If using FXML for layout, you may prefer to set the layout info like height and width there. If you do so, you could set the min and max values for the width and height all to -Infinity. This value is a convention in JavaFX for a sentinel value that uses the preferred width for other values. Such a setting is not possible with CSS, so, here I just set those values explicitly to the preferred size values.

RegionStyling.java

import javafx.application.Application;
import javafx.geometry.Pos;
import javafx.scene.Scene;
import javafx.scene.layout.HBox;
import javafx.scene.layout.Region;
import javafx.stage.Stage;

public class RegionStyling extends Application {
    @Override
    public void start(Stage stage) {
        HBox layout = new HBox();
        layout.setAlignment(Pos.CENTER);
        layout.getStyleClass().add("layout-pane");
        layout.getChildren().addAll(
                createIcon("user-icon"),
                createIcon("notepad-icon"),
                createIcon("cardiac-arrest-icon")
        );

        Scene scene = new Scene(layout);
        scene.getStylesheets().add(
                RegionStyling.class.getResource(
                     "region-styling.css"
                ).toExternalForm()
        );
        stage.setScene(scene);
        stage.show();
    }

    private static Region createIcon(String styleClass) {
        Region icon = new Region();
        icon.getStyleClass().addAll("icon", styleClass);

        return icon;
    }

    public static void main(String[] args) {
        launch();
    }
}