"Hey boss, this guys a fucking Nazi and we should not serve him. If we keep serving him it could get out on social media and we'll be accused of being Nazi sympathizers."
If your boss still doesn't care, out the bar on social media yourself and look for a new job.
I would approach your boss about it, but address it the exact way Nadia did in his post. Not necessarily a "I don't feel comfortable serving him," in case your boss doesn't give a damn about what you prefer to do or not do, but frame it in a way that he could stand to lose a lot of money and it be super-bad for business.
Be like "Man, do we really want word getting out on Twitter that this is where he hangs out? Protests outside the door, bricks thrown through windows, boycotts and poor Yelp! reviews... We could take a real financial hit because of this guy."
Your boss could be a decent guy, but he could also be a shithead who doesn't care about minorities, racism, fascism, or anything like that. I guarantee that if he's the latter though, he still cares about money and the prospect of losing it might make him take some kind of action.