I believe the founders were extremely aware of the influences of religion on government.  They remembered well the history of church rules during the era of witch burning under the decree of the church.  They made no provision to allow religion alone to become the foundation of laws. 
We currently have a number of religions in the country that control dress, the marriage of you girls to old men, the banning of young males, they don't allow outsiders with their circle of members. Maybe you've heard of the Old Believers, the Amish, the Quakers, the Hasidic Jews, some of the religious communes around the country.