Citizenship is a federal matter, not a state matter, so it is unclear how this would be enforced (it appears they would deny birth certificates, which is very odd). But even if they are able to get the logistics straight, this is still a federal matter.
The rationale behind this is to prevent "anchor babies" where parents will not be deported if their kids are US citizens. However, anchor babies are more myth than fact; you cannot deport a US citizen but you can deport their parents, whereupon they would become a ward of the state.
In any case, a child born here deserves to be a US citizen. Think of it this way: your parents are illegal immigrants from Mexico. You are born in the states and raised in the states. When you are 15, your parents immigration status is uncovered. Now tell me this, is it ethical to deport someone who likely speaks English as good as anyone else and has never known another country?