You can use "currentColor" as the color value in SVG elements, to pick up the color attribute from CSS. For example:
<div style="color: red;">
<svg viewBox="0 0 100 100" xmlns="http://www.w3.org/2000/svg">
<rect width="50" height="50" fill="currentColor" />
</svg>
</div>
<svg viewBox="0 0 100 100" xmlns="http://www.w3.org/2000/svg">
<rect width="50" height="50" fill="currentColor" />
</svg>
</div>
Note that this doesn't work when you're using an external SVG as a background image.
Final thoughts
Before finding this, Google gave me a bunch of misleading results. Here's hoping that improves.