Ignoring the Constitution, I think it is a great idea. Here's how I would do it.
Each morning, class would start with a prayer from one of the world's stronger religions.
A curriculum teaching these religions in turn, along with a unit on the less populated ones, would be written.
Getting the curriculum would not be easy, especially with all the divisions within each religion.
Hopefully it would help reduce intolerance. I have a girl friend who was taught in her Protestant religion that Catholics were the children of Satan. And for years Jews were taunted for being Christ Killers. Never mind how Muslims are treated today. Sikhs were killed after 9/11 because ignorant men thought they were Muslims. My brother was denied his milk and cookie when he refused to say the Lord's Prayer (it was in the mid 50s).
Of course, it won't happen. Despite claiming they are men and women of faith, meetings will break down into petty squabbles. Nothing (k)new. Just look at the battle over the Nicean Creed, and although written in 325 the Arian "heresy" still exists. Law suits will fly in court after court.
But I still wish that humans could agree on what is positive.