People who were into eugenics and "race purity" and "racial hygiene," as the Nazis were, thoguth segregation and anti-miscegynation (laws preventing the marriage of people of different races) were necessary in order to prevent "racial admixture" which they thought would be detrimental to civilization ("race suicide" was the common phrase). In other words, they would have seen it justified on biological grounds. They obviously would not have questioned that African-Americans were the "inferior" race in this equation.

If you want to get an idea of how someone like Hitler viewed the world, take a look at Madison Grant's The Passing of the Great Race, Or the Racial Basis of European History (1916), a book by a New York lawyer, philanthropist, conservationist, anthropologist, and eugenicist that Hitler called "his bible." It is a fairly cogent exposition of Nordic theory, which is just a hop away from Aryan theory. It talks at lengths about the need to segregate "worthless race types," to sterilize them, to ultimately "eliminate" them. Grant himself helped advocate for anti-immigration legislation in the United States, and for anti-miscegynation laws, including the 1924 Virginia law that was the one eventually overturned by the Supreme Court in 1967.