Interesting article over at the Claremont Review of Books. (NOTE: "interesting" ≠ "right".)
Seems there's a plausible interpretation of the 14th Amendment whereby birthright citizenship applies only to those over whom the United States has exclusive jurisdiction - so excluding not just children of diplomats but also (e.g.) those who have birthright citizenship elsewhere, based on their parents' nationality.
Which is material for ponderment, if nothing else. I'd always assumed otherwise.