Everyone has a culture. Even in America, who have someone from Boston and someone from Georgia even though they are both American, they would exhibit great differences in almost all aspects.
However, If both those people are white and you compared them with two blacks from the same regions, you would see a lot more in common with a white Bostonian and a white Georgian. This would be the more basic underlaying cultural aspects of being white. There are common cultural differences amongst blacks and whites just as well as sub-cultural differences amongst each race. Maybe I’ve mis-interpreted your point, but I don’t see how acknowledging black culture would be a problem if white culture is widely accepted in America?