Much of the wording of those historical documents resulted from 'the language of the time.' It had dearly little to do with abiding to a belief in any other authority than the governance of the people elected to lead the country.
Never once, did the US Constitution ever intend to replace The President, Congress and Courts with sovereign authority of a church of any kind. For God sake they just finished fighting years and years of war to rid themselves of entanglements with royalty that demanded 'the subjects' worship one god in one church. Whatever gives the Right Wing political elements in the USA the idea they can actually 'ride' the rest of the country for the sake of Socail Conservative values and completely disregard the values of others? What the heck? And people are actually voting for these 'icons' of deception? Wow.