It's an extension of tribes, and I think God did have something to say about that.
What you are saying is that given certain assumptions common to our society, certain people have a natural right to citizenship. Which is true. But those assumptions themselves are human inventions, not natural laws.
They are observations noted by the writers on Natural Law, whom the Delegates and and Ratifying legislators mention by name. Grotius, Puffendorf, Vattel, Wolf, Locke, Bynkershoek, Barbeyrac, Hobbes, etc.
The Romans would have agreed with you. Except they believed some men were "natural born slaves." Law of Nature.
IOW, you agree with me.
IF one accepts the opinions of the Enlightenment thinkers you mention, then one can reason to a conclusion as to who is NBC.
But the opinions of those thinkers as to what constitutes Natural Law are exactly that, their opinions. They are not facts. Other thinkers, with other basic assumptions, could come to different opinions on what Natural Law is. And those opinions, in and of themselves, would be neither more nor less valid.