“Non-Jewish” music covers a lot of ground. It runs from old-fashioned classical (Bach & Beethoven, through 20h century like Stravinsky and Debussy) through some of the obscenity-laced raps of people like Eminem and his mentors and the “white-supremacist” rock groups. Let’s get specific.
Classical? Why not (excluding music intended specifically to be religious, like masses and whatnot).
Old time popular (pre-rock)? Most of it is OK, even if it seems obsessed with (clean) romance. So it depends.
Classical rock? Again, it depends on the song.
60s rock? Many of the songs not, since they have pritzusdik lyrics. Still, some are OK.
Metal, rap, etc.? Definitely not. Some of this stuff would have been considered unprintable/unplayable back in the day.
Which brings us to modern “Jewish” music. Except for the words, which have been changed, a lot of it seems to have been simply lifted from secular sources. (Trust me – I’m an amateur musician myself.) In fact, some of the “Jewish” music played at chasunehs these days is musically more extreme than most rock. “Barbaric” is the adjective that comes to mind. Not to mention the ear-damaging volume. All of it, of course, with a rock back-beat behind it.
So we really have to consider the inyan – “non-Jewish” according to what standards? So much of what passes for Jewish music these days isn’t really Jewish at all, we’ve got to think a little further than just whether the musician wears a yarmulke.