For me, it's generally about the way the song is presented. The whole package, so to speak. I realize that's kind of vague so I'll try to shed a little more light on it.
I primarily listen to country. I enjoy a wide genres of music, but country is my number one. I am not a huge fan of rap, hip hop or metal. Yet I enjoy Linkin Park because of how they present their lyrics in the music. For me, I will generally listen to any song, if I happen to like that song, regardless of the singer or the genre. Back to the country genre, there are even country singers I don't like, and specific songs that I don't like by singers that I DO like. It's probably like that for many people.