From the Wikipedia page on the SC ruling, which had to do with women’s suffrage. In discussing that, the opinion went over the matter of who was a citizen:
“The opinion (written by Chief Justice Morrison Waite) first asked whether Minor was a citizen of the United States, and answered that she was, citing both the Fourteenth Amendment and earlier common law. Exploring the common-law origins of citizenship, the court observed that “new citizens may be born or they may be created by naturalization” and that the Constitution “does not, in words, say who shall be natural-born citizens.” Under the common law, according to the court, “it was never doubted that all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives, or natural-born citizens, as distinguished from aliens or foreigners.”[12] The court observed that some authorities “include as citizens children born within the jurisdiction without reference to the citizenship of their parents”—but since Minor was born in the United States and her parents were U.S. citizens, she was unquestionably a citizen herself, even under the narrowest possible definition, and the court thus noted that the subject did not need to be explored in any greater depth.[13]”
https://en.wikipedia.org/wiki/Minor_v._Happersett
The case doesn't help Cruz, unless a person uses intellectual dishonesty to twist the case.
The case does have some bearing on the question of NBC status for native-born persons, as well as on just plain citizen status for native-born people.