mg, I agree with you about writing new words to other well-known songs, when one set of lyrics is so strongly associated with the tune that most of your audience can't help making the connection. An example is a contemporary Christian hymn set to the tune of "Edelweiss." When I hear that, I can't help thinking of the lyrics to Edelweiss.
But in folk music, there are many tunes that have numerous sets of lyrics sung to them (e.g., the tune of "Tramps and Hawkers," to which I know at least 3 different songs, or the tune of "The Wreck Of Old 97" to which I also know several -- and don't get me started on "Great Speckled Bird" / "I Am Thinking Tonight Of My Blue Eyes" / "The Wild Side Of Life / It Wasn't God Who Made Honky-Tonk Angels").   And it's sometimes unclear which lyrics were the "original" ones.   I can readily accept new lyrics to such tunes -- especially when all the parodies are included.

But I do find it a bit disingenuous when someone says "Here's a song I wrote" and then proceeds to sing new lyrics to the tune of "Wild Mountain Thyme."