That's correct, according to this website and if it were purely a Democrat or Republican issue then that might provide protection. But the Nazi and White Supremacist angle muddies the water and will likely provide the employer with all the cover they need for the termination.
My understanding of legal arguments makes me think this assertion won't impress the judge. But of course in California, there is a very good chance you will get a Liberal Judge, and they will make a "hate speech" exception to the California law.
Nowadays the law means what judges want it to mean.
There’s an important grey area when it comes to “at will” terminations. While there’s a list of things you still can’t fire someone for, you can fire someone just because you decided to fire them. HR and company lawyers are generally very strong to make sure managers in “at will” areas know to never give a reason for the termination, because any reason you give could be spun into one of the forbidden reasons. But if you stick to “their services were no longer required” in all documentation you’re safe.