I really haven't delved into this subject, but I have a theory

Maybe the kind of racism that SS Germans hold is different from the racism that is prevalent in the US.

The SS would view any non-Aryan, meaning most Americans, on the same level regardless of skin tone. Blacks from Missouri, Metis, Cajun, Mennonite would all be the same.

So the KKK would have their panties in a twist about the black Americans on staff, crying that Braun hired animals, while Braun would be confused because from his perspective, he only has animals to hire.

This could be a very funny key and Peele sketch, like a no true Scotsman but who's more racist.

Again I haven't looked into the Nazi perspective justifying their racism so I might be way off the mark.