7. In principle, such state laws could be preempted by federal law, and I’ve heard some suggest that such firings might be called for by workplace harassment law, on the theory that the very presence of a known white supremacist or neo-Nazi employee would create a “hostile work environment” for nonwhite or Jewish employees. But I don’t think that would be a viable defense for the employer.
I do think that hostile environment harassment law can sometimes pose serious First Amendment problems (because it involves the government pressuring private employers to restrict speech in the workplace based on its content and viewpoint); and some, though by no means all, of the few courts that have considered the issue have likewise said that the First Amendment may preempt hostile environment harassment claims in some situations. But whatever one thinks of that debate, I’ve never seen any case that holds employers liable for a supposedly hostile environment created by an employee’s off-the-job political speech (at least when the speech isn’t specifically targeted at the employee’s particular coworkers). There’s thus no conflict between federal harassment law and these state speech protection laws, at least when it comes to off-the-job speech.