If the female met the requirements in the current statute (below), the child does indeed have birthright citizenship (which is the same as natural born).
"A child born abroad to one U.S. citizen parent and one alien parent acquires U.S. citizenship at birth under Section 301(g) of the INA provided the U.S. citizen parent was physically present in the United States or one of its outlying possessions for the time period required by the law applicable at the time of the child's birth. (For birth on or after November 14, 1986, a period of five years physical presence, two after the age of fourteen, is required. For birth between December 24, 1952 and November 13, 1986, a period of ten years, five after the age of fourteen, is required for physical presence in the United States or one of its outlying possessions to transmit U.S. citizenship to the child.) The U.S. citizen parent must be the genetic or the gestational parent and the legal parent of the child under local law at the time and place of the child's birth to transmit U.S. citizenship."
I’m continuing to grapple with these questions, and have been doing quite a bit of further study of the matter.
I’ve learned enough to know for sure that there are vast periods of American history in which someone born in Cruz’s exact circumstances would NOT have qualified as a citizen at birth, and therefore could not, under any rubric, be considered as a “natural born citizen.”
When the naturalization laws have been changed by Congress, has that somehow amended the Constitution or something?
But this does not apply to an aspirant for the presidency as it discusses citizenship, not Natural Born Citizen. Not the same.