Yeah, a clear difference between this joker and Hannibal, Freddy Krueger, Jigsaw, and even prior jokers is that this one, from previews anyway, appears to be a very sad, ordinary, struggling man who nobody notices and who has no meaning until he snaps and starts killing people. We don't have movies all about those other popular villains being sad, struggling, ordinary men until they snap and find meaning in mass murder. They aren't portrayed as relatable characters the way this joker appears to be.
Given all the shootings occurring in real life right now, a movie that makes that kind of protagonist at all sympathetic is concerning to some people - especially since we've already had one mass shooting by someone who said they were inspired by the joker (if I remember right.)
Nobody had these concerns about the DC joker, for example. It's very much a reaction to the way they're portraying, and potentially glorifying, the joker's origins as something relatable and accessible.
Edit: good point by The Lost that the joker didn't inspire the aurora shooter. The NY police chief told that to the media after the attack and it was widely reported, but he'd apparently made that up and the Denver Post had an article about that a few years later:
https://www.denverpost.com/2015/09/18/meyer-the-james-holmes-joker-rumor/amp/ Thanks and gig'em