"Nobody would ever have heard of me without them. They made me rich!"

 This is precisely the problem. Many nonwhites struggle to make ends meet. They struggle to get people to pay attention. Only when a white person appropriates their culture do the [white-dominant] society at large pay attention.

Why is it that many whites can only support a cause when a white face is attached to it?

 Would you be okay if you, a struggling artist, had your work copied/knocked off by a successful artist, who makes even more money off it while you remain poor?

 In an ideal society, BB King wouldn't need the Rolling Stones to make him popular/rich. But, in this society, whiteness is a privilege above all else, and it will make you successful faster than anything else.

Nonwhites, sadly, must beg for scraps and hope a white person helps them out just like the RS did with BB King.