I think you are conflating between a so called Natural Born Citizen, and a birth right citizen. Good example is Governor Jindal. His parents were NOT US citizens when he was born. Yet he is a birth right US Citizen.
What Trump has said is that he is against so called anchor babies, who are children born to illegals. I also do n ot like children born to tourists given US citizenship. That is a big business in China, when pregnant Chinese citizens arrive on a tourist visa, give birth on US soil and that child is automatically given US citizenship.
Very very few other countries are so generous in handing out citizenships.
Jendal is an anchor baby....Citizens born to foreign nationals regardless of status (See your Chinese birth tourists) are CINOS. Citizens in name only regardless of the actual rule of law.
I would suggest these stateless gorons of foreign nationals get naturalized.....So they don't get deported. :) /s In my dreams.