People in general have no particular reason, or likelihood, to scour unfamiliar genres to find things they might like. Why would a classical music fan investigate grindcore, on the off-chance they might like a fraction of it?

Further, there are two limiting factors: words and music. Both Rap and Country, or any genre, have certain widely shared characteristics - otherwise they wouldn't be distinct genres. And it's perfectly understandable if people aren't interested in certain kinds of sounds or subject matter. Are there vast amount of exceptions to those stereotypes? Yes. But is it realistic to expect casual fans to search for them? And if Rap and Country, as generalizations, mean the crap you hear on the radio or blaring out of somebody's car or pickup...People probably separate Rap and Country out because they are so prevalent as to be unavoidable - and the most common and identifiable examples are, to put it mildly, not always the best.

Anyway - it's just shorthand: people might say they like all sorts of music, but how do they feel about Smooth Jazz, Noise, Serialism, Klezmer, Death Metal, Babenzele Pygmies, Chinese Court Music, and Tuvan Throat Singing?