Protecting Religious Students from Vaccine Mandates Act of 2021 This bill requires public institutions of higher education (IHEs) to provide for a religious exemption from COVID-19 vaccination requirements. Through December 31, 2024, a public IHE that has a COVID-19 vaccination requirement must (1) provide a reasonable opportunity for individuals to receive a religious exemption from the vaccination requirement, and (2) notify individuals who are subject to the vaccination requirement about the procedures to apply for the religious exemption. An IHE must submit an annual report to the Department of Education certifying that the IHE meets these requirements. An IHE that denies a religious exemption to 20 or more individuals during a calendar year must provide additional information. The bill generally prohibits an IHE from receiving federal funds if it does not comply with the religious exemption requirements outlined by this bill.