?..why can’t an atheist/agnostic believe in personal liberty...? What would preclude it...?
They certainly can. Most people believe that it is inappropriate to steal from or kill others as well, but still we need a higher authority to prohibit those who do not.
Belief that our rights descend from our creator provides an authority on a higher level - not every man or woman elected to higher office may be inclined to hold those truths self evident to us, so the Constitution provides the required clarity.
It all comes down to moral law.
If moral law has no greater source than man, then the nature of that law is necessarily subjective.
In other words—without God, all moral law is nothing more than opinion. There is no ultimate groundwork for individual sovereignty.