They were aligned on more than one topic.
Hitler’s views were anti-Christian as well and he expressed admiration for Mohammedanism. There is enough indication that that could have been a religion aligned with Nutzi interest.
The other half of your argument “Do you think either of those things would have happened if the war went the other way? Of course it is impossible to know what other, unanticipated negative consequences would come with it and which outcome was ultimately better for humanity....but it is pretty easy to say that this outcome is the most “left” of the two options.”
—> Nothing about burning books. The Nutzis did that as did their fellow socialists, the Commies.
Nutzism was National Socialism and was socialist and centralized in its structure.
I fail to see which part of your argument has been ignored
The main maladies affecting our nation and our culture are:
1.) Invasion of foreign peoples and foreign cultures
2.) Our own culture has become depraved, debauched and indecent.
The Nazis, despite all of their other negative attributes, were NOT in favor of either of those things.
The first books burned in Germany were ones that advocated sexual immorality and transsexualism.