That would be a terrific story, except it's just that - a story.
Since AT LEAST 1898, the law of the land on birthright citizenship has been the Supreme Court case United States v. Wong Kim Ark, 169 U.S. 649 (1898). In it, the Court holds that anyone born in the US subject to the jurisdiction thereof, irrespective of the citizenship status of his/her parents, is a citizens of the United States.
They are not citizens because of statute, but because of the 14A. No statute, like your ridiculously absurd "law at the time that the child's citizenship followed that of the custodial parent" can disenfranchise a person from a right that they enjoy via Constitutional law.
If you are a citizen at birth, you cannot lose your citizenship, nor can your parents by design or neglect, renounce your citizenship either. There is ample case law since Ark that says just that.
"..If you are a citizen at birth and a minor child, you cannot lose your citizenship, nor can your parents by design or neglect, renounce your citizenship either.
"That said Wong Kim Ark has not, either by himself or his parents acting for him, ever renounced his allegiance to the United States, and that he has never done or committed any act or thing to exclude him therefrom."
MR. JUSTICE GRAY, after stating the case, delivered the opinion of the court.
The facts of this case, as agreed by the parties, are as follows: Wong Kim Ark was born in 1873 in the city of San Francisco, in the State of California and United States of America, and was and is a laborer. His father and mother were persons of Chinese descent, and subjects of the Emperor of China; they were at the time of his birth domiciled residents of the United States, having previously established and still enjoying a permanent domicil and residence therein at San Francisco; they continued to reside and remain in the United States until 1890, when they departed for China, and during all the time of their residence in the United States, they were engaged in business, and were never employed in any diplomatic or official capacity under the Emperor of China. Wong Kim Ark, ever since his birth, has had but one residence, to-wit, in California, within the United States, and has there resided, claiming to be a citizen of the United States, and has never lost or changed that residence, or gained or acquired another residence, and neither he nor his parents acting for him ever renounced his allegiance to the United States, or did or committed any act or thing to exclude him therefrom."