It's not white supremacy, it's the fact that they are Nazis. The very word Nazi is an acronym for "National Socialism". They ARE leftists.
The left wing Main Stream Media wants us all to call them right wingers and we fall for it.
It's wrong and it makes us legitimate right wingers look bad if every time they call bad guys right wingers and get away with it, even when it's simply not true.
As I said to someone else, when you actually study the pre-Nazi and Nazi eras of Germany, it is NOT a left-wing movement.
Again, there may be mutations of it that one could consider left-wing but it isn't leftist.
The populace who supported the Nazis were lower middle-class, small businesses and militant nationalists. They never established a base of support in the Social Democrat/Communist stronghold of the 'working class.' The Nazis were militantly anti-Bolshevist and viewed it as a Jewish conspiracy. They were also fervently against the Social Democrats, as well. The older nationalist figures and parties supported them or lent financial aid at various times, hoping to use Hitler as a pawn for their own schemes.
They were opposed to 'modern' capitalism but not (ideologically, at least) opposed to the old 'craftsman capitalism' that was fading away under industrialization and mass manufacture.
Nazi ideology was also highly mystical, reliant on pagan notions of an ancient and glorious past, an eschatological vision of a racially-pure future for "aryans." Now Communism is eschatological too, but not all such religions should be considered "leftist."
You must also remember that the Northern Nazis(I think, I might be confusing North/South) were defeated in an internal power play, and they were the more 'socialist' of the Nazi Party.
But as all totalitarians do, they went against their pledges(to a degree) and everyone came to be highly regulated in their daily lives.
Maybe it's best to think of them as a bizarre hybrid of both.