Protect Communities from a Porous Border Act of 2021 This bill requires the Department of Homeland Security (DHS) to notify a state before placing an alien in that state and gives the state final authority to prohibit such a placement. At least 10 business days before placing (e.g., detaining or housing) such an individual in a state, DHS must provide certain information to that state, including (1) the individual's biographic and biometric information, including DNA; and (2) a certification that the biometric and biographic information has been checked in various law enforcement and counterterrorism databases. No federal court shall have jurisdiction to review (1) the requirements and procedures established under this bill, or (2) a decision by a state to prohibit the placement of such an individual in the state. The bill also prohibits any federal official from waiving any of the bill's requirements.