Under present law in the two countries, I believe he has dual citizenship. Unless one of his parents has diplomatic immunity.
Does a child born abroad to U.S. citizens not owe allegiance to the U.S.?
Well, there's a pretty prominent example in history. W. Churchill. Mom was an American citizen, Dad a Brit politician. He had dual citizenship till he was 21, when he had to choose one or the other. If Cruz is eligible to be President, then presumably Winnie would have been had he chosen to be an American.
Will the courts similarly rule that it’s okay if a U.S. citizen goes to China to commit treason against the U.S.? That it’s not a crime because it wasn’t committed within U.S. jurisdiction? Will the courts rule that said U.S. citizen can return to the U.S. free and clear of all criminal prosecution because the illegal act didn’t occur on U.S. soil?
I think you're mixing up issues that have nothing to do with inheritance of citizenship. But I'm no lawyer, and I'll leave it to those who are to answer your questions.
“””Under present law in the two countries, I believe he has dual citizenship. Unless one of his parents has diplomatic immunity.”””
So when does one country’s jurisdiction end and the other’s begin? Or is such a person with conflicting allegiances also subject to conflicting jurisdictions and conflicting laws which may or may not be adverse to one of the countries involved?
“””I think you’re mixing up issues that have nothing to do with inheritance of citizenship.”””
No, it’s a question of jurisdiction. How is a matter resolved when there is an issue of countries’ conflicting jurisdictions?