The irony of people calling the current crop "Nazi" is that the original nazis probably would have looked down on them as thugs and untermenschen.
Ok so is it still ok to punch the ones that say "I'm a fucking nazi" or does that hit the same slippery slope?
It wasn't okay to begin with. You'll have committed an assault, and he'll have committed free speech.
If there is a mistake here, then the onus is on them to come out and say "hey, though we were acting like nazis and even calling ourselves nazis at various points, we don't actually want to eradicate non-white people, and think hitler was a dick" otherwise fuck 'em all.
Just so you know, actual nazis didn't want to eradicate non-white people. They considered non-Germans to be inferior, but not necessarily bad to have around in general. A lot of the most evil things that happened were not necessarily because they were thought of as philosophical goals, but because they were economically pragmatic and not philosophically prohibited. Of course, the line is a bit blurry in some cases, most famously with the concentration camps, where there were certain classes of people whom it was seen as desirable to separate from society, and then it became economically pragmatic to no longer keep them alive. But still, the motivation is being mischaracterized here. Lebensraum does not, after all, translate to "extermination".