Not as such, but if someone has undeveloped tastes in everything artistic in additionl to their bad musical taste, then it could be a problem. At best it means there are unlikely to be many shared cultural interests, and at worst it suggests a lack of intellectual/cultural maturity. If they just listened to pop music in isolation then that wouldnt be a dealbreaker but if you combined that with only watching Hollywood films, reading best seller novels, etc then it starts to add up.
In general I'd say that I dont care whether someone likes the same thing as me as long as they have the maturity to form their own tastes and at least make an effort to analyse what they like. Music is a fairly abstract artform so its more subjective than film/literature/etc, so its hard to judge people's character based on their musical tastes - liking bad music is usually more to do with not having much musical education/exposure rather than having bad values/taste. With film/literature its different since those are more explicitly about values, although if someone (eg) only liked ugly music (rap, punk, etc) then you could perhaps infer something about their character (not that there is anything wrong with ugly music as such)
In 99% of cases though: no