> How about breaking down by religion or something else that at least points to what kind of media/message the group is more exposed to?

I'm an American that fits into neither of these groups but nearly everyone I know does, so from my third party perspective I think you might be underestimating how different the sources, messaging, and conversations are between white and black Americans on average. That being said, I think it is still vastly overused in polls, and is perhaps a self-fulfilling prophecy to some degree.