"Christmas is a Christian holiday, and should be respected as such"

Christmas is also a Federal holiday. Christmas trees, Frosty and even Santa Claus have no connection to the religious aspects of Christmas and many non-Christians celebrate every year without a thought to Christianity.

Putting up a tree is engaging in celebrating a holiday sanctioned by the Federal Government not an admission that you believe in Christianity. Now if you put out a Nativity scene, that is certainly Christian-themed.