Real Education and Access for Healthy Youth Act of 2021 This bill requires the Department of Health and Human Services (HHS) to establish grants to support sex education and sexual health services for young people (ages 10 through 29) and repeals requirements that apply to certain federally funded sex education programs. HHS must award grants, in coordination with the Department of Education, to (1) provide sex education to young people through elementary and secondary schools, institutions of higher education, and youth-serving organizations; and (2) train education professionals to effectively teach, and otherwise support, sex education. Sex education refers to high quality teaching and learning that follows, to the maximum extent practicable, specified educational standards; covers a variety of topics concerning sex and sexuality; explores values and beliefs about those topics; and helps young people gain skills to navigate relationships and manage sexual health. Additionally, HHS must award grants for the provision of sexual health services to marginalized youth to youth-serving organizations and health care entities that are eligible to receive covered outpatient drugs at reduced prices through the 340B drug discount program. Recipients of any of these grants must comply with certain nondiscrimination requirements. In addition, they may not use funds for sex education programs or sexual health services that provide incomplete or inaccurate medical information or fail to address specified issues. The bill also eliminates prohibitions regarding the content of specified federally funded sexual health education and information programs and repeals the Abstinence Only Until Marriage program.