Why did the founding fathers leave out religion in the US Constitution?
First of all, we should be clear that the Founding Fathers did not completely leave religion out of the Constitution. They stipulated that there should be no religious tests for holding office. The First Amendment guaranteed freedom of religion. So religion is not left out completely. Instead, it is more accurate to say that the Founders simply did not establish a religion.
The reason for that is that the Founders felt that religious conflict was a major source of problems. They knew, of course, about how many problems religion had caused in English history. They knew of the Catholic-Protestant problems around the time of Queen Elizabeth I. They knew of the conflicts between the Puritans and Anglicans in the English Civil War. They also knew that there had been conflicts between Puritans and others (for example) in some of the colonies.
From this history, the Founders knew that conflicts over religion could do much to pull a country apart. Therefore, they wanted to ensure that no religion could ever have official status so that there would not be any fighting over whose religion would be the official religion of the country.