The founders barely gave any thought to citizenship or naturalization.
The "subject to the jurisdiction thereof," almost certainly referred exclusively to Native Americans, because even way back then, it was generally recognized that although they lived in the territory of the United States, they remained their own sovereign nation, sort of without territory, some with reservations of various types and flavors and some without. So even though they may have been born in the territory of the United States, in some abstract way, it was as if they were born in another country, within our country. And to attain US citizenship, had to undergo naturalization.
This wasn't wholly an act of disrespect, either. Many Natives didn't want to be regarded as citizens of the US without some overt action on their part.
The sovereignty of Native Americans on reservations, and reservations themselves, have become gradually more and less formalized, but even today, we recognize that Indian tribes may have many of their own laws and jurisdiction to enforce them. But we also passed the Indian Citizenship Act in 1924 that undid that aspect of the 14th Amendment. And, in keeping with the foregoing, some tribes were opposed to it.
Trumpco is trying to extend that notion, that Native Americans were only partially subject to the jurisdiction of the US and therefore not citizens by birth, to citizens of any nation. It kind of fits in an abstract way, but I don't think was at all what the drafters of the 14th Amendment intended.
Also, there is a "common understanding" of birthright citizenship under the 14th, but only a handful of legal decisions explicating it. And as was the usual case with century-old decisions and statutes, a bit of ambiguity.