I'd say there was plenty of reasons to do so, and far more reasons to SHOOT one.
Violence begets violence. You, or me, or anyone else beating up or shooting a Nazi will only perpetuate their nonsensical pseudo-reality of white victimhood. You will make a martyr that only exacerbates the problem.
But when you make it abundantly clear that their ideology will get them fired, ridiculed, and shunned they are much more likely to change their ideology. It won't change the staunchest Nazis - and those people will inevitably end up imprisoned when their belligerent ideology leads them to the wrong side of the law - but the privileged brats that think being "alt-right" is fun(/ny) will realize that..."Oh, words have consequences."
I'm by no means condoning the ideology, but some "alt-right" grew up in insulary environments that prevented them from interacting with people of color, or differing ideologies where everyone is considered equal. I grew up in the south, I've met these people. They talk about racist views as casually as you or I would buying groceries. It's a disservice to them to not at least attempt to enlighten them. And if that doesn't work, and if law enforcement won't step in to prevent them from enacting their violent rhetoric - only then is it justified to punch a Nazi.