(a) Person born to foreign diplomat —
(1) Status of person. A person born in the United States to a foreign diplomatic officer accredited to the United States, as a matter of international law, is not subject to the jurisdiction of the United States. That person is not a United States citizen under the Fourteenth Amendment to the Constitution. Such a person may be considered a lawful permanent resident at birth.
Being born here to two parents subject to a foreign jurisdiction makes you a foreigner.
I described that difference earlier, and has been in the law since about 1804.
You point describing children of diplomats applies ONLY to children of diplomats.
See: Inglis v. Trustees of Sailor's Snug Harbor 28 US 99
That is, the party must be born within a place where the sovereign is at the time in full possession and exercise of his power, and the party must also at his birth derive protection from, and consequently owe obedience or allegiance to the sovereign as such, de facto. [Footnote 7] There are some exceptions which are founded upon peculiar reasons and which indeed illustrate and confirm the general doctrine. Thus, a person who is born on the ocean is a subject of the prince to whom his parents then owe allegiance, for he is still deemed under the protection of his sovereign and born in a place where he has dominion in common with all other sovereigns. So the children of an ambassador are held to be subjects of the prince whom he represents, although born under the actual protection and in the dominions of a foreign prince.