Too bad that's not what the 14th amendment says.
“The Fourteenth Amendment begins, "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."
The key phrase to consider there when considering who is a "natural-born citizen" is "subject to the jurisdiction thereof." The argument of Trump's legal supporters is that illegal immigrants are
subject to a foreign sovereignty, are therefore not subject to U.S. jurisdiction, and thus the citizenship clause above does not apply.
The "subject to the jurisdiction thereof" clause, ignored by birthright citizenship advocates, has to have some meaning or it wouldn't have been included, and the number of children of foreign diplomats being vanishingly small, we can assume it extended beyond that extremely rare case (so rare as hardly to be worth mentioning).
What was meant by the clause was that you had to be
subject to no other sovereign.
Senator Jacob Howard drafted the citizenship clause of the Fourteenth Amendment. Here is what he said it meant: "This will not, of course, include
persons born in the United States who are foreigners, aliens, who belong to the families of ambassadors or foreign ministers accredited to the Government of the United States, but will include every other class of persons." (Emphasis added.)
Well, if we value honesty, that right there should settle it.
Congressman John Bingham, sometimes called the father of the Fourteenth Amendment itself, held that its meaning was that "every human being born within the jurisdiction of the United States
of parents not owing allegiance to any foreign sovereignty is, in the language of your Constitution itself, a natural born citizen.”