I mean… The Joker is regularly portrayed as being a fan of eugenics and other fascist philosophies.

Their tropes are a bit different. Joker’s MO is to try and convince people that they’re just as fucked up as he is right before he eggs them on to do some kind of Saw Movie tier horror, while Red Skull likes to think he’s simply better than everyone else and entitled to pull the trigger himself. But they’re both sociopaths and serial killers. You don’t get bonus points for being Antideutsche while giggling your way through a massacre.