What constitues Jewish music?
Whenever this discussion is had, people throw around exclusive criteria. Authorship, composition, and performer, style and content are all mentioned as *THE* criteria for deciding what Jewish music is. The categorization has consequences, after all, some won't listen to non-Jewish music. So let us briefly examine some of the criteria offered, and then offer an explanation as to the definition of Jewish music.
Performer/Authorship/Writer: Music is classified as Jewish if the author or writer of the lyrics is Jewish. Anyone can quickly refute this, would you consider Israeli-pop music Jewish? Or Barabara Streisand? Not to mention that many performers don't write their own music. And many of the writers are Jewish, performed by non-Jews, yet we don't consider it Jewish. Additionally, does anyone consider Mendelsohn Jewish music? Or Kenny G? Jewish authorship is not the key.
Lyrics & Content: What if the words are taken from Tehillim, Gemara, or other Jewish sources? Not all Moshav, Blue Fringe or Avraham Fried songs are pesukim. Many people won't sing pesukim, but their music is no less Jewish. Is "For every season" Jewish? Koheles is definitely a Jewish sefer. And of course, I doubt any would consider a song by Creed, a Christian rock group, to be Jewish music, even if the song didn't mention their savior.
Surroundings: One of the arguments against Shlock Rock, Blue Fringe, Moshav, etc is that they sound too much like English pop music. But historically, Jewish music has always borrowed from the surrounding culture.
Yiddin, usually performed at weddings, is originally a German song.
When looked at broadly, Jewish music doesn't consist of any category other than where it is performed and who it speaks to. There's no reason the Beatles or Billy Joel can't be considered Jewish if the message is correct. Likewise, Blue Fringe or Avraham Fried are not automatically "Jewish" music. Rav Yehuda Amital, Rosh Yeshiva at Yeshivat Har Etzion once said that the only time he paskened like R. Nachman m'Breslav was on this issue, that music doesn't have tumah, regardless of its origin. Immediately after, he joked that if R. Nachman heard some modern pop music, he might change his mind.
So when someone says they don't listen to non-Jewish music, its really a cultural thing, music that hasn't made it into their subset of the community. It can't be placed into a category, and attempts to categorically defend it are useless. What it does mean is that both sides, those who do and those who don't listen to "non-Jewish" music, are missing the boat. One side is being pragmatic, defining it based on current cultural standards of what is accepted within the community. The other, while trying to couch it in absolute categorical terms, is really using it as a mask to attack a certain societal and cultural view. So what we have is both sides being ignorant or (worse) deceitful. Which makes it hard to have a discussion.