I need you to focus on this phrase: “…cultural/historical milieu the Holocaust took place in.”
while also understanding that the Holocaust didn’t occur in the United States
You missed my point. The concept of Jews being white isn't a historically new phenomenon and goes back before the 1900s. Nearly every instance of ethnic cleansing, you have the perpetrators using physical traits to separate themselves from those they want to extinguish. The Hutus also saw themselves as a different race from the Tutsies. Was the Rwanda Civil War a race war? Of course not, yet the intentions of the Hutu would say so. You can even find Jewish propaganda that claims they are a different race from Palestinians. Thus Hitlers intentions were to use any reasoning, even if irrational, to push his agenda. Thus his bogus idea that Jews were a different race should be discarded, as they weren't even consistent with the classifaction and definition of race in that time.
