Honestly, I never get why government schools decide to use Christian tropes and then complain about them at the same time. Just avoid the music rather than butcher it. Really, just stick with "Frosty the Snowman" and other related gibberish.
Some Parents Upset After L.I. School Removes Religious References From ‘Silent Night’
In a related story, apparently at least one Veterans Administration hospital considers singing Christmas carols to patients to be "spiritual care" and, thus, bans a high school choir.