Note that 1st amendment applied to Federal Gov. States could, and did, have official religions. Not sure how comfortable we are with that idea, but it does make sense. If we are bothered by a NY religion, we can move to Montana and get enough votes to make it into an Uganda or a Birobidjan. So, under this system, there would be no problem having 10 comm in a state school.
Only later expansion of right to state governments created a current system. It also, I think, hallowed out state governments and lead to the current, unhealthy, state where democracy is hinging on an election of all-powerful President who is the head of an all-powerful Federal machine.
If we were to still have strong states, people would stop freaking out about federal elections.
As to 10 comm in public schools – just give everyone vouchers and the problem will be solved.