They are citizens thru jus solis i.e., birthright citizenship. They are issued passports and have all the rights and privileges of any citizen of this country. Congress would have to pass a law to change it and if it fails to pass constitutional muster, we would have to pass a Constitutional amendment. Scholars differ on what would be needed to change the current practice that is part of US Code.
The 14th applied to freed slaves and the children of slaves.
>>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.<<
Actually if born to Mexican parents, they are Mexicans, which makes them subject to the laws of Mexico.