I think there's an argument to be made that such children aren't citizens. But in light of the 14th Amendment, and particularly in light of the way in which it is worded - "subject to the jurisdiction of the United States" - I think it's a weak one, and I seriously doubt it would stand up in court.
I disagree. There have been several rulings by U.S. Secretaries of State stating EXACTLY such in denying U.S. citizenship to those born in the U.S. to temporarily resident aliens, AFTER ratification of the 14th Amendment.
In the case of Friedrich de Bourry, born in New York on December 4, 1862 to an Austrian citizen father who was only temporarily in the U.S., the U.S. Secretary of State hit the issue right on the head. He ruled that de Bourry WASN'T a U.S. citizen at birth because his father WASN'T a U.S. citizen at the time, NEVER made the requisite declaration of his intention to become a citizen prior to Friedrich's birth in the U.S., or in any way signified his intention formally to ABJURE his Austrian allegiance. Born in the U.S. but NOT a U.S. citizen at birth due to failure to meet the requirements for birthright citizenship.
Obviously, legal immigrants would have already made the requisite declaration of their intention to become U.S. citizens thereby signifying their intention formally to ABJURE their foreign allegiance. Legal immigrants' children born in the U.S. are citizens at birth, though not necessarily 'natural born citizens' for the purpose of Constitutional Presidential eligibility.
And have there been any since 1898? Can you name even one?
When it comes to a Secretary of State, versus a federal court, federal court trumps.