I dont think mozart or bach is any better than whats on the radio nowadays. Also the words to these songs are problematic, they are not the only issue with goyish music. A rabbi once gave a shmooz that the person who created the beat and tune to these songs “neshama” enters these beats and infiltrates yours, I’m sure nobody would want to be affected by these recording artists dirty souls.
Now if your going to get into songs that have dirty words and meanings, the problem is clear. How can one hear these disgusting lyrics and fantasies and then learn gemara the next day the same way he would if he had not heard the song. And the songs that may sound clean usually have some underlying message that you cant dig up from the surface.