Protecting Financial Privacy Act of 2021 This bill prohibits a federal agency from creating, implementing, or administering a program that requires financial institutions or individuals to report on the balances of, transactions involving, or transfers into and out of financial accounts. This prohibition does not apply to laws or regulations in effect on September 1, 2021, or to the Bank Secrecy Act (laws that require financial institutions and other entities to report on certain financial transactions to prevent money laundering, the financing of terrorism, and other criminal activity). This prohibition does apply, however, to regulations issued under the Bank Secrecy Act after September 1, 2021.