Who gets to say who are subject to the jurisdiction?
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside
Rephrase the sentence. All persons born or naturalized in the United States are citizens of the United States and of the state wherein they reside and are under the jurisdiction of the United States.
That does not change the meaning of the sentence and explains who says who is under the jurisdiction.
John / Billybob