Right. Just as our U.S. rules on citizenship are part of our municipal law. See Perkins v. Elg, 307 U.S. 325 (1939)("municipal law determines how citizenship may be acquired").
the Framers, in matters of citizenship, looked to the law of nations.
Wrong. Story didn't say that. Go back and read more carefully.
the other side's citing Shanks
If that presidential eligibility case entailed someone born outside of the U.S. (like Cruz) why on earth would anyone be citing Shanks, a case that involved a person born in South Carolina?
And if that eligibility case were brought against someone born in the U.S. (e.g., Rubio), the attorneys for Rubio would cite U.S. v. Wong Kim Ark, a case making abundantly clear that our citizenship rules are founded on English common law (a case in which Shanks is cited by the majority in support of that point).
It might be simpler if you take some of the straw men which seem to be inhabiting your brain, paint different colors on them, and let them battle out this fictitious argument.
As to Story's opinion in Shanks: Here is precisely what he says on point:
"The incapacities of femes covert provided by the common law apply to their civil rights and are for their protection and interest. But they do not reach their political rights nor prevent their acquiring or losing a national character. Those political rights do not stand upon the mere doctrines of municipal law applicable to ordinary transactions, but stand upon the more general principles of the law of nations.
Perhaps it is you who should read more carefully. What Story holds applies not just to the question of what "natural born citizen" means in the Article II eligibility clause but to the broader category of the law of political citizenship as a whole. Thus, according to Story, who was the acknowledged expert at the time on the subject, what was said in English common law did not apply to this broad category just because it was set out in English common law. You have asserted that Story did not say what I have just shown that he clearly said. The argument for Cruz' meeting the presidential eligibility requirement relies upon the leap from the fact that the Framers were familiar with English common law that is what they had in mind when they chose the language for the eligibility clause. What Story held does not support that leap in reasoning.