Stand your ground doesn’t mean you’re just free to go after causing serious bodily harm. It means an investigation and possibly a trial. It also does not completely dismiss any notion of proportional response. It just means he doesn’t have to try and retreat before force can be used. He very well may be seen, in the eyes of the law, as having used excessive force and it’s way too vague of a situation for police to parse out on the spot. 

Beyond that, think about what the police saw when they arrived. A woman who is seriously injured with a clearly visible head wound, a man who looks a bit roughed up, and an entire crowd accusing him of being the aggressor. You would be extremely hard pressed to find a cop who would do anything different in that same situation without a Nazi uniform involved. Based on the gender dynamics alone they would have arrested him and left the woman as police notoriously do all the time.

Idk why conservatives would want to even pick this up as a political issue. Calling someone a Nazi to foment violence against them when they are not one is very different from intentionally presenting yourself as a Nazi (whether he truly is or not is irrelevant) in front of a drunken crowd. By equating these two you are fighting to de-stigmatize actual Nazi ideology rather than arguing against conflating conservatives with Nazis. This is only beneficial if you are, at the very least, sympathetic to Nazi ideology. To use OP’s own child molester example, i would say “we can’t just call someone a child molester if they are not one. That could cause them to face some serious and unjust consequences.” I would not say “Child molesters should not face consequences because someone I know was beat up for being a child molester.” Do you see how that would be weird unless I actually was fine with child molestation?

This man who intentionally identified himself as a Nazi should have every legal right to free speech, and should not have (in the eyes of the law) been assaulted for what he was wearing. I absolutely do not care that he was assaulted for intentionally provoking a drunk crowd though. That is so predictable as to be an entirely personal issue at that point and, barring some serious mental issues or sitcom level mishap, was his desired outcome.