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.