I can't stand grunge/alternative/anything too heavy on the "rock side." The loudness, screaming, and concentrated anger can just be too triggering for me. It's kind of a shame because I know some of the lyrics are great. I think I would identify a lot with these genres if they didn't get me so worked up, haha.
On the other hand, I do like music that, as someone above said, dares to say things that may not be socially acceptable. I really like Kimya Dawson for this. Her sound is beyond mellow (almost reminds me of a camp sing along), but she says some really surprising things.