Aside - I have a huge problem with the implication that rap only became popular when melanin-deficient people started listening to it.
Black music has been dominant in America since jazz. Jazz was appropriated by white audiences. The same thing happened with rhythm and blues and its derivatives. I don't think there's a single turning point where white audiences decided to start listening to Black music. I'd say Motown was pretty important in terms of popularly producing music that was embraced en masse by a white audience that recognized they were listening to music created by Blacks. Of course, that was around the time of the civil rights movement, the 1960s counterculture... aka a big change in social values.