I think the best way to put it is to rehash a old saying: Hate the song, not the singer.
Yes, that policy doesn't work with some singers, but for teen idols like her, Justin Bieber and even Miley Cyrus, all they're doing is living their dream, or doing what they feel they're good at and making money off of it. Now, don't get me wrong, I wouldn't care to listen to music from any of them, though that's mainly due to the fact that their music isn't my style. I prefer classic rock and heavy metal. Thats just me.
However, while I don't hate them and only mildly dislike their music, what I hate is their fans. There comes a point when fandom goes too far, though that applies to everything.
Bottom line is, someone out there likes their music, and if you don't, you aren't required to listen.