Among many problems with Trump's citizenship executive order (such as its obvious conflict with the constitution) is a practical one: birth certificates, which are currently the primary proof of citizenship for those born in the US, are issued by state and local authorities. These agencies do not (and aren't equipped to) determine or record the immigration status of the parents.

This means that citizenship would no longer be established with a US birth certificate or any other primary document.

In practice, birth certificates would likely be accepted MOST of the time as establishing citizenship, but those listing parents with "foreign sounding" names would be subject to open-ended scrutiny and investigation. And years later, people born here whose parents are dead or unavailable might have no way to definitively prove that they're citizens.
@mattblaze that sounds like part of the plan!