Music written by Jews is Jewish music. The only authentic holy Jewish music (of which I am aware) is that of the Leviim in the Beis Hamikdash. Everything else comes from anywhere that Jews have lived or travelled, or listen to in their surroundings. We cannot HELP but be influenced (the Maoz Tzur we sing, for example). To negate the coming together of musical notes, because it might have a non-Jewish origin, makes no sense to me (unless it is IMO really awful music, like certain types of heavy metal or jazz, which I personally do not much like), because we are continuously influenced by the world around us. And that is not necessarily a bad thing, musically.
When I first heard the Moditzer album, as a young(er) person, my first thought was that it reminded me of ANY march I had ever heard, though personally it was more melodious to me BECAUSE IT WAS MODITZ. It is the meaning behind the music that makes it worthwile. When I hum a “Jewish” tune that might have been secularly-based, I am not thinking, “WOW, what a great secular song!” I am thinking of how this song resonates with me, and that brings me closer to Hashem, especially if the lyrics are from Tehillim.
People can think and believe whatever they are comfortable in thinking, but for me, there is only MUSIC, neither Jewish nor non-Jewish. It is how we take the music and elevate it to a level of Kedusha, that makes all the difference. Just my very humble opinion.