The Constitution of the United States does not discuss anything about holidays. No incompatibility there.
The Constitution of the United States does not discuss religious paraphernalia, other than it can't be banned. Putting up a town Christmas tree is not unconstitutional. Neither is putting up a town Menorah or any other religious symbol. Many government builds have swastikas on them. They are part of the building facad. They are a religious symbol too.
A prayer to a god is not unconstitutional. There is nothing that describes whether that god exists or what the character of that god is.
Why not? If they want to haul them to school and there is room enough in the classroom for them physically, that's their issue, isn't it?
I really don't care. That has nothing to do with the Constitution of the United States. It's no different than a lot of churches putting a cross on their roof.
You claim to support the Constitution of the United States, then you turn right around and condone banning a particular religion (Muslim) based on personal opinions.
Just what are you trying to argue here?
BTW, the 1st amendment applies only to Congress, not the States. However, States have similar wordings in their own constitutions. States have in the past established religious tests for holding office, banned certain religions, etc. Currently, no State does so.