HTML uses color whereas SVG uses fill and stroke. You can get fill or stroke to use the value of the color CSS property by using the value currentColor e.g. fill="currentColor"
Define the fill: of the whole SVG as currentColor in the CSS:
svg {
fill: currentColor;
}
This makes the whole SVG to inherit the normal CSS color: of the surrounding element. Just make sure that all SVG child elements don't have any fill defined.