Making Education Affordable and Accessible Act of 2021 This bill reauthorizes through FY2027 and revises the Fund for the Improvement of Postsecondary Education (FIPSE) program. The bill also authorizes new grants under the FIPSE program. Specifically, the Department of Education may award grants to institutions of higher education for dual or concurrent enrollment programs or early college high school programs that allow high school students to earn postsecondary credits.