filee - your posts have left me not a little confused. I haven't gone back and reread them so apologies if I get some of this slightly wrong.
Firstly - this is a Nativity play. Not a 'winter celebration' as you have said a couple of times. A Nativity - a Christian play about the birth of Jesus, the Son of God. It is exceptionally religious, no two ways about it.
Of course, most parents aren't all that religious or Christian, but they know that Christianity informs a lot of our culture, traditions, art, literature, and so are happy for their children to learn about it (though they don't want the children indoctrinated, which is of course a different thing altogether). Those who actively don't want their children to take part of course have the right to request that they are excluded, and, like the OP, can do so.
Now, I don't work in a school so perhaps it is possible that teachers should contact parents who have done this to run past all celebrations such as harvest festival, Christmas and Easter* past them. Seems to me like that could take up rather a lot of a teacher's non-existent free time, particularly if they end up in the kind of ludicrous back-and-forth that is happening here. But yes, I guess, in theory, they could.
However, and this is what you seem to be missing - exactly the same should be done by the parent. They should think through, find out for themselves, exactly what would be involved in a request to withdraw their child from religious activities at school. And then put that down in writing - no to religious education and assemblies, yes to Nativity play. But you seem to want to absolve the OP, and indeed any parent who makes this request, of any responsibility for their actions. You say the child's feelings should be thought of - certainly they should, first and foremost by their own parents!
*Easter. That non-Christian celebration that is, globally, far far more important than Christmas. I'm thinking Latin America particularly. The rising of the Son of God. No, that's not important or religious at all. The fact that the early Christian church tacked their celebrations on to existing pagan celebrations doesn't change a thing. Winter and spring solstice aren't Christian, Christmas and Easter are. Is that really so hard to comprehend?
Oh, and finally, if my child (and I hope she does) learns about Eid and Diwali and Hannukah at school, and there is any kind of activity or play involved (I'm afraid my knowledge of these is pathetically sketchy) I certainly wouldn't expect those festivals to be downgraded to allow her to take part.