> But I don't think you can say "a group that calls itself socialist has at least this one left-leaning trait" isn't a position reasonable people can disagree on.It is to anybody actually familiar with the history of the NSDAP. The "socialism" in their name was mostly PR, what little socialist currents existed in the early NSDAP, represented by the Strasser brothers, was bloodily purged during the Night of the Long Knives.
It's for that reason the very first victims in the concentration camp Dachau were not just Jews, they where German leftist political opposition Jews: Communists, socialists, antifascists, killed as early as 1933. The very same reason why Nazis considered the communist USSR as their arch-nemesis.
> What I find worse than people going both ways on wether nazis are left or right leaning, is someone in a position of authority like wikipedia saying, one side is objectively right [about a question that isn't even rigorously posed] and will be treated as such.
All this information can be found on Wikipedia, not just there, but also local Wikipedias from the places it actually happened. Like the Fuerth Wikipedia being even more in-depth and detailed [0], which is the city next to Nuremberg, both very relevant places for the early rise of Nazism.
That's why it's really not this "open debate" you make it out to be. The only people who insist on that are usually US Americans, due to the caricature "atheist socialist leftist" boogeyman that's been peddled to them for decades and some Eastern Europeans with post-communism shock, to justify their ideological hard shift to the right into often straight up fascism.
[0] https://www.fuerthwiki.de/wiki/index.php/Rudolf_Benario