I think what causes this argument in the first place is that there are somewhat different definitions in the US and Europe for “leftist” and “rightist.”
While Hitler didn’t posess the (apparent) love for all races that US liberals claim to, he did take state control of almost everything. So there is a socialist element there although not the same as European socialism.
Of course Hitler stole some ideas from others! He also stole the “Hitler Salute” from the Italian fascists! In fact, that’s the old Roman salute! And the phrase “Heil Hitler” was also stolen from the Romans! “Ave Caesar” means “Heil Cesar”!
Hitler did take state control of almost everything because he was a DICTATOR, not because he was a Socialist or whatever! Same fits for Stalin. He was a DICTATOR, so he naturally took control of almost everything! But their politics are DIAMETRAL OPPOSED!