I like many "popular music" songs -- but they have melody, harmony, and good (at least neutral) lyrics. And if they entire lyrics would fit into a Twitter feed (140 characters or less), then forget it!
Cranberries, Counting Crows, Jon Secada, Gin Blossoms, etc.
These were on the radio back in the early 90's when I was a teenager. Some songs I used to listen to I no longer like; others I still like (they must have objective value!)
Your typical "popular" song tends to discuss problems in the world today, without offering any real solution. Artists tend to be the most sensitive to problems in their own time.
I think many Catholics (sometimes secretly) enjoy some of these kind of songs, though the artists/bands leave a lot to be desired as far as their personal lives. Let's face it, these popular singers/bands fill a void left by folk music, which isn't very alive today. We don't have any other culture to fill that void, for the most part.
But Classic Rock is pretty clear-cut. Plain, unadulterated "Rock & Roll" -- which is short for "Rock & Roll around in the hay." is another story. I think a Catholic pretty much NEEDS to cut out certain bands, no matter what their personal preferences or "feelings". KISS, AC/DC, and dozens of other "hard rock" and "classic rock" groups would fall into this category.
It's simply not music, and it's not innocent. The lyrics are filthy. I've seen the titles of many KISS songs (a relative used to listen to this trash). Double-entendre doesn't begin to describe it. No, they leave little to the imagination, and that's just the song titles!
That would be like me trying to justify listening to "House of Pain" (an Irish gangsta rap group) just because I used to listen to it. I was stupid when I was 17. I was also in the target demographic for gangsta rap music (white, teenage, middle-class male) But, objectively speaking, it's bad music, bad lyrics, and a Catholic shouldn't listen to it. Let's just say these guys don't rap about how chaste they are, how monogamous they are, or how forgiving they are. So I got rid of that CD when I started getting serious about living my Faith.