Beating up his girlfriend doesn't make his music worse or worse. It makes him a terrible person, but it doesn't affect his music.
I'm (and so is the general pop-audience, it seems) of the firm belief that you can, at least to a large degree, separate the music from the musician, the art from the artist. Sure, they're not completely separate, neither in how they're made or how they're listened to, but one does not stand and fall with the other. There are plenty of musicians who seem like total jerks who's music I still enjoy, just as I like music from people that I admire for other reasons as well. I don't think anyone is ever going to look up to Chris Brown as a person, but he didn't become famous for being a nice guy in the first place, so It's not too surprising his career is still going.
As for how he's famous despite his music being cwap? It's radio pop, that's just how it works.