Restoring Board Immunity Act of 2021 or the RBI Act This bill grants antitrust immunity to state occupational licensing boards in states that satisfy specified occupational licensing law requirements. These include (1) requiring a board's actions to be authorized by a non-frivolous interpretation of the state's occupational licensing laws; and (2) using less restrictive alternatives to occupational licensing to address threats to public health, safety, or welfare. Such states must either establish an office to supervise boards or provide for judicial review of occupational licensing laws.