I called for a trial to assess if his words are true, and yes, I would be okay with capital punishment for enthusiastic participation in genocide. Was Nuremberg a slippery slope?
You seem to be rushing not to take him at his word, to the extent that he shouldn't even be investigated for it and should just be charged with harassment, even though there's an active genocide going on and it's entirely plausible that he has murdered numerous innocent people as a participant, and he is claiming that he has.
The harassment is obvious, but it's trivial compared to what he claims to have done. What he claims to have done should be investigated. If true, he should face the consequences of those choices.
Fine if you disagree about capital punishment for crimes against humanity like mass murder and genocide, but there's nothing civilized about seeing a Nazi on the street saying he's killed many people in the camps and plans to kill more and just saying "He should really be more polite. We have rules about that."
If he's just a loudmouth, fine, but at least investigate his claims and prevent him from killing more people if his claims are true, whether it's by capital punishment or by long-term imprisonment.