Rights for the Transportation Security Administration Workforce Act of 2021 or the Rights for the TSA Workforce Act of 2021 This bill modifies the workplace rights, protections, and benefits applicable to Transportation Security Administration (TSA) personnel. Specifically, the bill within 180 days, eliminates personnel authorities of the Department of Homeland Security (DHS) and the Department of Transportation governing the conditions of employment for TSA employees, thus making TSA employees subject to the personnel management system applicable to other federal employees; sets forth transition rules that protect the pay rates, leave rights, and other rights of TSA and Federal Air Marshal Service employees; and requires DHS to consult with the labor organization certified by the Federal Labor Relations Authority to carry out the conversion of such positions. The bill also directs the TSA to implement in-person or remote mental health programs at each field office of the Federal Air Marshal Service and consult with labor associations to address concerns regarding federal air marshals, including mental health and suicide rates; requires DHS to prioritize the hiring of veterans, including disabled veterans; and directs the TSA to ensure its employees are provided proper guidance regarding prevention and protections against the coronavirus.