Sure, theme components added to a theme will use that theme’s color scheme and ignore their own.
What this means is you can:
- Create a theme
- Add your customisations to it.
- Add it to as a theme component to all your active themes you want to use it on.
- Magic.
That way, the theme component (tag colors in your case) will be active on all the themes you added it to without needing to copy the css to all the themes.