Vaccine Passport Prevention Act of 2021 This bill generally prohibits governments from issuing vaccine passports (i.e., standard documentation other than health records to certify an individual's COVID-19 vaccination status to a third party) and discrimination based on an individual's COVID-19 vaccination status or post-transmission recovery. Specifically, the federal government may not issue any vaccine passport or discriminate based on an individual's COVID-19 vaccination or recovery status by requiring documentation of the status as a condition of receiving a benefit or service. In addition, the federal government (except for the Department of Defense) may not mandate COVID-19 vaccines as a condition of federal employment. Furthermore, the bill prohibits, as a condition of receiving certain COVID-19 relief funds, states, tribal nations, and localities from issuing vaccine passports or engaging in discrimination by requiring documentation of an individual's COVID-19 vaccination or recovery status. Additionally, the bill prohibits private entities that offer products or services affecting interstate commerce from requiring documentation of an individual's COVID-19 vaccination or recovery status in order to obtain a product or service. It also establishes a private right of action for individuals who experience such discrimination by private entities. The bill also provides an exception to allow kindergartens, elementary and secondary schools, and institutions of higher education to mandate COVID-19 vaccines as a condition of enrollment. However, the Department of Education may not award financial assistance to any school that requires COVID-19 vaccines without also providing for exemptions based on (1) religious or conscientious beliefs, (2) medical reasons, and (3) natural immunity from COVID-19.