^I think I understand what you're saying, except that the same CHRs that use the tagline "All The Hits Without The Rap" have Bruno Mars and Taio Cruz on the top of their playlists, and they avoid Eminem along with black rappers, so I think it's clearly a style of music issue rather than a race issue
Just speaking for myself, I'm not a big fan of rap, and it has nothing to do with race - I just grew up playing guitar and piano, and I like to hear music in songs rather than just beats and spoken words - and when rap hits come out which are more musically-centered (like Airplanes, Just A Dream, and Love The Way You Lie), I listen to them constantly
I'm just assuming that lots of other people feel the same way, and that's where the "no rap" thing is coming from, rather than from race