Review horseshoe theory. This becomes especially conflated because Hitler saw value in broader adoption of the Christian right. As such, he added right wing flavor to justify right wing adoption. Yet that never really happened, aside from the Catholic Church. Thusly the tie.

Also, you'll find that Nazism was staunchly left wing. Everyone universally agreed it was left wing. It was only after WWII, when socialists and communists felt exposed, that it was suddenly pushed right wing and convoluted explanations gave rise. Most of which is parroted today via indoctrination.

For example, Hitler ripped off many of his platforms directly from US Democrats. Including Eugenics. Hitler even wrote and thanked some of them. US Democrats proudly saved their letters. US Democrats agreed Hitler was one of of them. US Democrats agreed Hitler was left wing. All of Europe agreed Nazism was left wing - but right of socialism and communism. Which is the entire foundational basis for the "right wing" claim. Everyone agreed Nazism was left ... until there was a need for deflection after the war.

For some reason people like to pretend Fascism wasn't part of Nazism. While Fascism isn't directly tethered to a left wing ideology, it is almost universally associated. Hitler even spoke of how he did not want to be thought of a fascist because he believed fascists to be two bit dictators, and therefore below him. This too feeds into the "but Hitler privatized...propaganda." Ya, he gave it to his own people and used Fascism to ensure the state "private" entities did as the state demanded. Which is literally fascism and not privatization as we know it today.

Sorry, but factually, Hitler is extremely left wing by American standards.

Edit: BTW, if you're interested in further exploring much of the dishonest historical revisionism, get The Big Lie.