I spent my last two years of elementary school in Idaho Falls, a town that was at that time 70% Mormon. In the public school the only Christmas songs that were permitted were purely secular ones with no religious references.
I spent high school in Hanover, NH, a town dominated by Dartmouth College and thus by liberal humanists. In the public school we sang the full range of Christmas carols, including religious ones.
This may initially seem surprising; one might expect religious songs to be more tightly restricted in the liberal humanist community rather than in the Mormon one. But upon reflection it makes perfect sense.
In Idaho Falls there was a serious danger of a religious takeover of just about every institution, public education included. For example, my Boy Scout group met in the Mormon church and was taught Mormon propaganda, contrary to the national organisations rules. (Though we also watched Dracula: Prince of Darkness in the church basement, so theres that.) Hence the secularists were motivated to fight tooth and nail to keep religious references out.
In Hanover, by contrast, there was no serious danger of a religious takeover of the public schools, so the carols were experienced as a cultural tradition rather than as the nose of a proselytising camel, and so were embraced.
I leave the moral as an exercise for the reader.