For the most part, I pretty much hate pop music, with a few exceptions.
First off, I'd like to say that change is a good thing. You can't expect a band to pick one sound and stick with it until they die. If they do, and they make it work, good for them. But just because they enjoy writing one way for the most part doesn't mean that they don't enjoy other music. It's one thing to change completely your music, it's another to dabble and make a variety of music.
I like a lot of hard rock and metal music, especially older stuff. Black Sabbath, Ozzy Osbourne, Gun's N' Roses, Iron Maiden, etc. I also like a lot of just rock music, like Tom Petty and John Cougar Mellencamp.
The reason why I really don't like pop music is because the focus isn't on the instruments. It's dead center on the singer. A good singer is important in any kind of music, but you also need good music. Most pop music is just a singer singing with some weird effects (auto-tune, echo, etc etc etc. [with are fine when used in moderation, but when everyone and their mom is doing it, it's just annoying and get old fast), a catchy beat, and the like.
When you listen to rock music, a good singer is cool (and important) to have, but the music really hits you, too.
I tend to clump bands like Green Day, Paramore, and The All-American Rejects into the alternative genre. While some of their songs are more poppy than others, these bands still have enough focus on the music to get me by. Hayley Williams is an amazing signer, but she's not the complete focus of the band.
I don't buy into the whole emo genre, all music is supposed to be emotional to some extent. Music can't be music without emotion, in my opinion.