Apply GaussianBlur or Pixelate to Polygon

This should work for you, it clones the original image, applies effects to the clone and then using an image bush fills a shape with exactly the right portion of the mutated image.

using (Image image = Image.Load("fb.jpg"))
{
    var outerRadii = Math.Min(image.Width, image.Height) / 2;
    var star = new Star(new PointF(image.Width / 2, image.Height / 2), 5, outerRadii / 2, outerRadii);

    // we want to clone our source image so we can apply 
    // various effects to it without mutating the original.
    using (var clone = image.Clone(p => {
        p.GaussianBlur(15); // apply the effect here you and inside the shape
    }))
    {
        // crop the cloned down to just the size of the shape (this is due to the way ImageBrush works)
        clone.Mutate(x => x.Crop((Rectangle)star.Bounds));

        // use an image brush to apply the section of cloned image as the source for filling the shape
        var brush = new ImageBrush(clone);

        // now fill the shape with the image brush containing the portion of 
        // cloned image with the effects applied
        image.Mutate(c => c.Fill(brush, star));
    }

    image.Save("output/fb.png");
}

This is an example of the final result:

This is and other samples are available in the ImageSharp samples repository https://github.com/SixLabors/Samples