The answer above is correct, style and script tags will get stripped before the rendering. But there is a trick: you can use an svg which supports <foreignObject> tag for rendering html and it supports <style>.
Checkout this repo which uses this trick to render css, this repo also features extra explanations
Since your html code uses external images, you will need to convert those images to base64 to embed it directly into the svg like this for the css:
background-image:url('data:image/png;base64,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')
and for the img:
<img src='data:image/png;base64,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'/>
Then your svg would look like this:
badge.svg
<svg fill="none" viewBox="0 0 160 23" width="160" height="23" xmlns="http://www.w3.org/2000/svg">
<foreignObject width="100%" height="100%">
<div xmlns="http://www.w3.org/1999/xhtml">
<style>
a {
display:inline-block;
background-color:#FC5200;
color:#fff;
padding:5px 10px 5px 30px;
font-size:11px;
font-family:Helvetica, Arial, sans-serif;
white-space:nowrap;
text-decoration:none;
background-repeat:no-repeat;
background-position:10px center;
border-radius:3px;
background-image:url('data:image/png;base64,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')
}
img {
margin-left:2px;
vertical-align:text-bottom
}
</style>
<a> Follow me on
<img src='data:image/png;base64,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'/>
</a>
</div>
</foreignObject>
</svg>
Then in your readme, use an <img> tag to render the svg, and enclose it in a <a> tag:
README.md
# test-repo
<a href="https://www.strava.com/athletes/94166049"><img src="badge.svg"></a>
Description of the repo
I've set up this example in this repo: https://github.com/bertrandmartel/css-readme