You don't think someone holding views to the effect that jews, gays and black people/slavs should be exterminated is a work issue? If I belonged to any of these groups and found out by chance that the person was a neo-Nazi, even if they never brought it up at work, I would certainly demand that they not work in my vicinity anymore. Then management would get to choose between me and a literal neo-Nazi.

The problem is, at least in my experience, that phrases like "neo-nazi" more commonly refer to Trump supporters, Republicans, edgy Twitter wags, etc and less to Mein Kampf reading would-be perpetrators of genocide.

The problem is when it’s not so clear-cut.

If I worked with a colleague from Iraq can they report me to HR for having been in the military and bombing their country?

I’m sure we can think of lots of cases where it is or isn’t easy to say yes to “report to HR”. It’s a tough topic and the answer to it changes over time and based on geographic social norms.