The way the laws are written definitely favor the employer, even in states like California. It is not easy to make your case against your employer, especially if they say you were fired for being a Nazi or white supremacist.
The ACLU made the case in the example of the Illinois Nazis way back in the 1970s, I think. They lost a lot of support for doing so, but they saw it as a necessary consistency of their position, and so they ended up doing it, and they won.
In Europe they have 25 different parties. The argument that protection must be restricted to only two parties is itself discriminatory and arbitrary.
Personally I don't give a D@mn what happens to @$$holes that go to Nazi type rallies, but as a matter of application of the law, I don't see how you can exclude them from protection just because they are bad people.
If we allow people to have the protection of the law removed from them because they are "bad", what are we going to do when the shapers of public opinion declare that Christians are "bad"?