Financial Institution Customer Protection Act of 2019 This bill specifies that a federal banking agency may not request or order a depository institution to terminate a customer account unless (1) the agency has a valid reason for doing so, and (2) that reason is not based solely on reputation risk. Valid reasons for terminating an account include threats to national security and involvement in terrorist financing, including state sponsorship of terrorism. A federal banking agency requesting a termination must provide the depository institution with notification and justification.