I thought the "Kyle's Mom" song was motivated by her campaign to ban "Terrence and Philip" and get the U.S. to declare war on Canada.
That was the second time it was sung. The first time was in the very first South Park Christmas special where they were trying to do a Christmas play and Kyle's mom complained because it had not only a Nativity, but also lots of Christmas decorations. She wanted all reference to anything Christmas, secular or religious removed. That's also the episode with the first appearance of Mr Hanky.