Our culture never will recognize God as the authority—furthermore, it never has.
Believers are “dotted across the landscape” as CS Lewis points out, they aren’t’ the majority of humans. Believers are several and few, but just like a single candle in a dark room light up the depravity and depravity does not like light.
It appears what you state is true in that the Constitution does not speak of/refer to God explicitly. However. the Declaration of Independence is explicit as to a God which is involved in human events. The Constitution was the social formalizing of the Declaration of Independence. As to sexual ‘deviancies’ I have never heard any person explain why life creations were created with obvious different sexual construction except those that do believe there is a master force ie God that created the opposites. .