Why is not liking something any more of a conversation stopper than liking something?
Ever heard of "Yes, and" in the improv scene? Giving a negative without then giving an out to the other person to keep talking puts the responsibility of finding a different topic on them. Do that several times, and people get tired of finding new topics.
Often when people ask you if you like X music, you can say that no, but I like these other music styles. That opens the conversation so they can find songs in your style they like and keep the conversation flowing. If they then trash you that's not on you tho.