Earlier quoted context omitted.
There's nothing to fight in court, in USA it's completely legal to fire someone for their political beliefs in the "at will employment" states. The argument against similar actions during Red Scare and Moral Majority is not that they were illegal but that now in hindsight we see that they were wrong , despite fitting the governing moral/political desires of the time, so similar acts should be avoided in future and pe…
How many years before we realise that denying the holocaust wasn't wrong? The problem with being fired isn't because of views then, you'd think people with views that would get them fired would be working to get those laws changed.
I.e. I'm think that making someone unemployable or outcast as a harsh (and perhaps even "cruel and unusual") punishment which should happen only for things the society has explicitly forbidden, and after we have properly established that the accused is actually guilty. Obviously, it's not the situation right now in USA (at least not in the at-will states), where employers have a wide (IMHO too wide) discretion of what they will tolerate for non-job-related acts of employees after work; some will fire antivaxxers, some will fire pro-vaxxers; some will fire holocaust deniers; some will fire people for having an OnlyFans account; etc. (and, crucially, they'll fire them for assuming they are like this, which won't always be true).
IMHO this discretion needs to stop, as it the case in some countries with different employment laws. And if we do want to have a harsher treatment for some of those things (e.g. holocaust denial is a good example) than for others, then that distinction should be decided in laws by the whole society, not unilaterally by company owners.