How about Deities, or characters that get their powers from Deities?
Any superpowered individual claiming to be a God or claiming their powers come from a pantheon of Gods, is going to stir up all sorts of problems by their very presence.
Punisher would likely not change too much in how he’s viewed, imho.
Law enforcement would officially see him as a him as a serial killer/huge threat, criminals would crap themselves at the thought of him, and ppl in general would be divided, w. some cheering him on, while others condemned his actions.