Federal Agency Customer Experience Act of 2021 This bill requires certain agencies to collect voluntary customer experience feedback with respect to their services and transactions. Each of the agencies must (1) annually publish such feedback on its website and report on such feedback to the Office of Management and Budget, and (2) report on the solicitation of such feedback. The Government Accountability Office shall publish a report assessing the data collected and reported by the agencies. The feedback may not be used in any appraisal of job performance of a federal employee.