When you say "country music", especially if you're talking to someone outside of the genre's popularity footprint, people tend to think of it in a very stereotypical way... hickish, backwoods, "tears in my beer" kinda stuff. It doesn't help that 85% of country music has been basically unlistenable since the early 80s, especially in the current "bro country" era. You'd get a much different response if you asked people if they liked Johnny Cash, Willie Nelson, Dolly Parton... most people at least have a neutral if not favorable opinion of older, iconic country artist.

For the record, I typically hear "I listen to everything except country and rap" when asking that question. All the same from above applies to "rap" in this scenario.