The authors of the 14th amendment make it clear that they meant subject to the total and complete jurisdiction of the USA. John Bingham even said what I have been using as my tagline since 2011.
"of parents owing allegiance to no other sovereignty."
Section 1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
The actual text, in relevant part, of the 14th Amendment. Any law or policy must be consistent with it.
I agree that the authors did not intend to give citizenship to the offspring of illegal aliens. However, their explanatory writings were not adopted as part of the Constitution.