Can't honestly think of any sort of music that I 'can't' listen to.
I struggle with talentless musicians, rap, hiphop, boy bands who sit about on Marshall amps attempting to convince the public that they have some guitar playing ability.
I do struggle with opera too, though I do enjoy classical orchestra music.
The biggest compliment anybody ever paid me was I was among friends in a pub, a song came on, somebody asked who the artist was and somebody replied, ''Dunno, ask eddy, he's into all the weird stuff'', (meaning ask me). Saying this summed his musical ignorance up perfectly, ergo, if he doesn't like it then it must be rubbish. And of course I knew who it was, I aren't ignorant, I appreciate that there is no such thing as 'crap' music, if it puts a smile on somebodys face, then all well and good.
Having said that, I do agree with what others have said here, X Factor offends me, its an insult to my integrity as a human being. Britains Got Talent, that cuts close to the bone too, was really glad when I read a dog had won it one year.