I think these HR systems also use "bad culture fit" to encode red flags they can't legally record: health issues, political disagreements. This already dubious mechanism can get further abused by badmouthing.
This is absolutely the case.
That said, you're probably not going to get fired over your politics unless you're either (a) seen as a union supporter (or, worse, organizer), or (b) so far right you've already been cancelled and are now a PR liability. If you're in the middle, they usually don't really care who you vote for, at least not enough to punish you for it.