I don't have a teen. So take this with a grain of salt.
I don't censor even for my small children. I do occasionally listen to the rap / r&b (generally quite ok) / hip-hop radio stations. I listen to all kinds of rock.
I would agree with MD on this one. For small children, I give a glossed-over explanation. For older children, I'd have a talk.
If there was another child involved, I personally think that adults who want to listen to something that offends another person should leave the room, rather than vice-versa. But that's a very cultural thing and so long as it's universal and fair, I don't think it matters, provided the other child has the chance to leave.
We all love Lady Gaga and whenever DD1 asks what she's talking about, I say, "Love." A half-truth at best but it seems to work. LOL!