Hitler wasn't a Fascist. Fascists are Italian socialists. Hitler was National socialist, which is kinda like Fascism, but super racist and German.
Government control of the market isn't a free market, nor is it privatization. If it's government control, it's public.
Karl Marx was an anti-semite too, but that doesn't make him right-wing. Socialism is inherently anti-semitic because it sees capitalism as Jewish. Which was actually Hitler's issue with capitalism, because he saw it as a Jewish plot to foster oppression of the working class, thus ushering in communism, which he also saw as Jewish.
What do you mean by "he supported critical race theory"? That doesn't seem like something he would agree with, though it is leftist.