I’ve found elsewhere that the b is to be capitalized when referring to culture but not when referring to a generalization. This is a more modern take which differentiates the Black minority experience of, specifically, American and British slave descendants. So one would say, "the Black community of Atlanta" yet "black Haitians". Thus White is to be capitalized when referring to American and British majority culture (usually followed by a descriptor like supremacy or privilege), but not the generality.
But this is splitting hairs on designations that are increasingly meaningless. Nigerian immigrants to America are often dismayed to find they are now Black instead of black. Just as someone from India and someone from Vietnam are both Asian, with almost nothing else in common culturally than the continent.
Any B v b or W v w debate is essentially quibbling racism, which pidgeonhole to stick someone in, further dehumanizing them. We would do best as writers to use either sparingly.