I don't think "should" or "shouldn't" are words that even ought to enter into it. In other words, it's silly to me when holiday decorations get turned into a right versus wrong issue by groups of people who seem to just want something to fight about. I wouldn't necessarily expect a school to put one up if they didn't wish to, but I can't imagine being sincerely offended by seeing one there.

I just found this article about a school actually taking away the Christmas tree and banning Santa:

"The principal of an elementary school in Ashland, Ore., has removed a holiday giving tree from the school after several families complained it was a religious symbol."
http://www.komonews.com/news/local/78647482.html

What's next? The Tree Police? Seriously, unless I were physically forced against my will to stand in front of the tree and stare at it, I fail to see the actual harm it would cause. I'm sure I could list all sorts of things in the world that don't particularly appeal to me, so what? If I don't like something, I can simply pass it by and ignore it. I am not a Christian, but I adore all the pretty decorations and music this time of year.