How exactly do you know an athiest by sight?
But getting beyond the willing suspension of disbelief (you'd have to have the kind of tyrant who thinks people only act moral with God in order to have a result like this- that's what makes it comical), I don't see how that changes anything about human rights.
At that point the social contract turns against my right to live or to have religious freedom.
That means for some reason society went retarded and decided these rights are superceded by some nonsensical ideology that athiests are dangerous or whatnot... similarly how we determine criminals have no freedom (if rights are inalienable, how do criminals lose them).
Why am I supposed to think God is a better answer? If this were the law, no amount of praying would change the fact that my life was forfeit (well... actually it might. If I prayed, people wouldn't think I was an athiest

). God is irrelevant.
So what does it all mean?
That no rights can be taken for granted. All of our rights are subject to the worldview of the population. This is true regardless of religion or political system. God does nothing to ensure rights. Nor does any constitution unless it has legitimacy with the people.
Not a very sunshiny answer, is it? If I say something is my right, it does not matter when the people decide I don't have it. I can try to fight for it, try to convince people. But I cannot make it so by asserting the name of any deity or political principle. Not unless people agree my interpretation.
But despite that, people do seem to be expanding freedoms to more people and as a result athiests are able to not practice as they see fit. Despite God not doing a (*)(*)(*)(*) thing to ensure rights and the constitution being just ink on paper, we do manage as humans to retain human rights rather well.