I think part of it also, is that the leftists tend to call us conservative types “Nazis”. And we know we aren’t Nazis, so we want to push back and say that Nazi is an acronym for National Socialist German Worker’s Party. And then to talk about the Nazi socialist roots.
I have not studied the minutiae of German National Socialism to know if there are fundamental differences between that ideology and Marx’s ideology. If there are some key facts we all need to know, please let us know.
Initially the German Nazi party was very socialist. The only major distinguishing features from the German Socialist\Communists was anti-Semitism & German Nationalism. There was effectively two factions in the German Nazi party: the “red” very socialist side & the “brown” side anti-Semitic motivated, nationalistic, not as “socialist” committed but most important fanatically loyal to Hitler. The “red” side was centered around the SA Chief Rohm, and a few others (Names I forget!) - Goebbels was sympathetic to it also. The “Night of the Long Knifes” and subsequent murder of Rohm & his lieutenants & suppression of the SA ended that. Goebbels was told to get with the program and he did.
The future Nazi Party was the German Worker’s Party when Hitler joined it in 1920. It was a tiny regional party featuring a grab bag of nationalism, antisemitism and anti-capitalism.
The anti-capitalism turned out to be rhetoric and it definitely wasn’t Marxism. When Hitler eventually took power over Germany the Nazis didn’t collectivize farms or take over industry. He even managed to sell off a few that the government owned. The actual German Marxist and socialist parties always regarded the Nazis as bitter enemies having nothing in common with them.
Hitler is one who renamed the party the National Socialist German Workers Party, the NSDAP. He lifted the name from already existing Austrian party, and people today pretending that ‘Socialist’ had some great philosophical significance to the Nazis are just being stupid. It was just a name, a borrowed one at that.
No one at the time thought it was a party of the Left. But it wasn’t of the Right either. It’s generally regarded as sui generis, a criminal regime controlled by a madman.
Shirer’s The Rise and Fall of the Third Reich used to be widely read. Less so are George Mosse’s books like Nazi Culture or his Crisis of German Ideology. But any familiarity with good histories would put an end of this current nonsense of trying to recruit Nazism as a bludgeon for scoring political points in 2020.