“...what citizenship one would more or less “naturally” assign to a person.”
Well, I know a lesbian couple that have kids together. Egg from one gal, fertilized, then implanted into the other gal. A year later they did the same but vice versa. So the term “naturally” gets screwed up pretty quickly. (Which one is the “real” mother?) Although I guess in their case the citizenship might be clear - both moms are American, and the children were born here.
Although - the status of the father/donor is unknown. What if it was/is a foreign citizen father?
What about the muslim invaders? Mom and dad are illegal in the country, have a child born on U.S. soil, raised and indoctrinated in the mosque? (Well - pretty close with that scenario at the present moment.)
In all of humanity's history up to the time of this country's founding, there were two ways to determine citizenship. One is by place of birth, the other is by citizenship of the father. It does get tricky when the father isn't know, if the rule applied is citizenship of the father.
Today, there are statutory rules that apply to children born of donor sperm.
English common law was that citizenship is determined by the place of birth.
Under law of nations, the rule of citizenship by birth in the invaded country doesn't operate. The child is not a citizen of the country being invaded (unless the invaders prevail and make the country theirs, then they make the laws).
US law would turn on how the phrase "and under the jurisdiction" (in thee 14th amendment) is construed. I'm of a mind that the phrase means the person is legally present but not a foreign diplomat. The prevailing view, the one expressed by SCOTUS in Wong Kim ark, is that the phrase means anybody present 9except diplomats), because anybody present can be arrested, has to follow traffic laws, etc.