Basically every monotheist religion shares the same moral guidelines, which, coincidentally enough, were the guidelines upon which our country is founded as well.
So in your world, you don't want any religious values informing law.
What, pray tell, would your standard be?
Your own mind, or someone else's?
Hint: Those are the only two choices left. So in a world which rejects all religion based morality, whoever is the big dog calls the shots. That's the way it ever was, and ever will be.
The objectivists have it figured out pretty well. I think the Founders would have approved. Well, Jefferson and Paine certainly would have. Maybe not Adams or Franklin.