In one of Rav Matisyahu’s books, he writes that words are the problem, not the music. So it’s not a problem to listen to Jewish music that is taken from goyish music, unless you know the real words and they are problematic (since you will think of the real words when you listen to the music).
One problem I have discovered though is that normally if I am somewhere where goyish music is being played (a bus or goyish store – although I try to avoid such places), I am usually able to block it out and not listen, but if it’s a tune that is used by Jewish musicians, I will end up hearing it and hearing the real words.