The way I understand what Jewish music is, it is “clean music.” Now if a person could find this “clean music” even if it was written by non-jewish artists that would fine besides for one problem. It is inevitable that one will start to listen to not so clean music and on. That is why people would tell you not too even start listening to non-jewish music. By making a rule that one should only listen to jewish Music would just be protecting ones self from all the shmutz that is popular.
I have heard from multiple sources that in the late 20th century the music on the radio was “clean” and one was allowed to listen. (other then kol isha obviously for a man) But now in days it is totally and completely Asur.(other then classical etc.)
In my opinion a person is able to listen to any music he wants if and only if the msuic follows under these 3 criteria.
1) If the music is considered “clean” according to normal people.
2)If the music you listen won’t lead you (in any way)to inappropriate content.
3) The music is not Kol Isha (for a man)