Political affiliation is a protected class under California law.

There are actually several US states that have political activities as a protected class. But you are correct for most US states, that is, employers in those states are free to say "All Democrats - you're fired!" and it would be legal.

It is in california, among other places. Federally, there are about 5 or 6 regulations covering workplace speech, the most sweeping of which is usually considered to be the NLRA.

If you google for nlra and lexology, you can see a number of articles about the scope.