Honestly, I think the issue is when the tune is from non-Jewish music and the words that are sung are just lyrics made up by the group. When the lyrics are from pseukim or something inspirational (not something that is just about physical relationships or other things against Torah), then the desire to slide back into non-Jewish music is less. By stopping to listen to all non-Jewish music for a period of time, like kkls45 said, you can usually eventually go back to a middle ground without getting pulled back to the other side again since it no longer has the same emotional connections for you.
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