The Articles of Confederation (the original constitution) left all religious manners to the states, so it didn't mention religion at all. Some of the states' original colonial charters were religious, others were not.

TBH, back then, there wasn't much Christian unity and very different perspectives on religious worship between say, the Puritans, Baptists, Presbyterians, Calvinists, Catholics, etc.

Many had fled Europe due to religious persecution from other Christians. The more recent constitution (from 1789 till now) gave us freedom of religion and association in the bill of rights to protect us from the government.