Lyrics rarely offend me. Even if content is problematic, I think it's a useful insight into a state of mind. Then again, I know there's some truly hateful stuff out there, but that's not something I seek out.
As for music itself, I tend to dislike rnb (I can enjoy the more modern stuff like Tinashe or FKA Twigs though), and jazz. The latter is partly the instrumentation, and partly the loose style that characterises it. So to expand, I also dislike loose, jammy or improvisational music. I like things very tightly composed.