[moehoward]

Exactly! Diplomats were the reason for the wording.

Senator Jacob Howard, co-author of the citizenship clause, does acknowledge the limitation, he also includes foreigners and aliens.

It is customary to put an "a" or a "the" (or "his" or "her" in connection with a King or Queen's subjects) before subject if one intends subject to be a noun.

"Every Person born within the limits of the United States, and a subject to their jurisdiction"........

Wouldn't that infer persons in the U.S. were the subjects? Clearly not the intent.

[BikerNYC]

It would read:

All persons born or naturalized in the United States and [a] subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.

It's pretty clear that the way it reads now means that, to be a citizen, the person who is born here must be subject, as a verb, to the jurisdiction of the United States. This includes all persons born in the United States except those who have immunity from prosecution, in other words, the diplomatic corps. I think that the meaning you give to these words is forced.