I should have said that firing an employee for expressing political opinions is GENERALLY not illegal. There is no federal prohibition, but state laws can vary.
In another thread, tbw2 posted with a very informative link about a somewhat similar case in New York. A law professor explained that there is some protection, but its scope is unclear, and the employer might be able to use one of the exceptions: https://reason.com/volokh/2021/01/27/may-n-y-businesses-fire-employees-for-using-parler-and-gab/
I didn’t know that California had also restricted the traditional employment-at-will rule. Perhaps, as j.havenfarm thinks, this employer still has the discretion to fire her, but at least it’s not as clear as I originally thought.
As stated neither of the two applicable statutes protects her