As others have mentioned, you can just use an inline SVG for the logo and have the CSS change the colour, e.g. with svg { fill: #colour }.
It's worth bearing in mind though about things like colour contrast, especially at smaller sizes. Light text on a dark background has less contrast than dark text on a light background. This can matter if the logo is very small or used as a favicon. However, CSS can help there too, by allowing you to change the size of elements, change the stroke width, etc.
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As others have mentioned, you can just use an inline SVG for the logo and have the CSS change the colour, e.g. with
svg { fill: #colour }
.It's worth bearing in mind though about things like colour contrast, especially at smaller sizes. Light text on a dark background has less contrast than dark text on a light background. This can matter if the logo is very small or used as a favicon. However, CSS can help there too, by allowing you to change the size of elements, change the stroke width, etc.