If one takes the view that the authentic right-wing in the West is orthodox Christianity, then Nazism is decidedly left-wing.
Its insistence on the primacy of the secular state over the Church, its hyperdarwinist placement of supposed genetic purity over religious devotion as the mark of human worth, its materialist doctrine of history, its Marcionist stance toward Jews and Judaism - it's a twentieth century melange of ideas concocted in the nineteenth century by decidedly anticlerical thinkers.
The most successful advocate of Nazism in America besides Margaret Sanger (a left-wing icon) was William Pierce, author of The Turner Diaries.
Have you read that book? It's a fictional work about how the protagonist starts a "resistance movement" that ends with genocide of all non-Aryans in America. At the end of the book, with the enemies of the white race all eliminated, the new Aryan government puts all its loyal Aryan citizens to work on collective farms and enters them into breeding programs to produce even more superior specimens.
In China, they call that Maoism.
Actually, I'm surprised you've never noticed the direct link between the father of liberal higher criticism - Adolf von Harnack - and the Marcionism of the Reichskirche.
The true defining line between Left and Right is very hard to figure out, since many on both extremes sound very similar even as they hate each other. I have theorized in the past that the line is universalism vs. henotheism, or equality vs. hierarchy, or atomistic vs. "organic" collectivism, or horizontal vs. vertical collectivism. I've long since given up.
Please don't be offended by my position. I used to belong to the Birch Society, and I find much of their message to be hogwash.
I’ve always thought that the Father of Higher Criticism was Spinoza.