I personally don't like Miley's videos or dress sense, but i don't stop DD (10) from listening to her songs or watching her videos. The only rule we have is "If Miley would wear it, DD doesnt". Does that mean I'd happily let DD behave the way Miley does.. eHell no! But like other's have said, the Miley the world sees is a fabricated image, much like a character in a movie. DD and I have spoken about this and she is smart enough to understand it.
As for Justin Bieber.. DD used to be a fan, but his public behaviour has turned her off him. I think he's headed for a lot of trouble.