If you read further in the Minor decision, they talk about the original naturalization acts in the United States, such as 1790 and 1804, in which the citizenship of children of aliens is dependent on whether the parents are naturalized. To me, this shows that our founders rejected the so-called English common law notion of natural born subjects. Second, if you read Shanks v. Dupont, they acknowledge you can be native born, but not be a U.S. citizen, depending on whether your allegiance adhered to the British crown. But even if you accept English common law, that the children of aliens could be natural born subjects, that was dependent on whether the alien parents remained in the country. Wong Kim Ark talks about this and it's why they make permanent residence for the parents a factor in determing that the plaintiff was a citizen at birth. Obama's father, of course, was not an immigrant nor a permanent U.S. resident, so he wouldn't even meet the Wong standard for being a citizen of the United States.
Good post ...