Repeal Existing Policies that Encourage and Allow Legal HIV Discrimination Act of 2021 or the REPEAL HIV Discrimination Act of 2021 This bill concerns the burdens that federal and state laws, policies, and regulations may place upon people living with human immunodeficiency virus (HIV). The bill directs the Department of Justice (DOJ), the Department of Health and Human Services (HHS), and the Department of Defense (DOD) to initiate a national review of federal (including military) and state laws, policies, regulations, and judicial precedents and decisions regarding criminal and related civil commitment cases involving people living with HIV. DOJ must transmit to Congress and make publicly available the results of such review with related recommendations. DOJ and HHS must (1) develop and publicly release guidance and best practice recommendations for states, and (2) establish an integrated monitoring and evaluation system to measure state progress. DOJ, HHS, and DOD must transmit to the President and Congress any proposals necessary to implement adjustments to federal laws, policies, or regulations. This bill shall not be construed to discourage the prosecution of individuals who intentionally transmit or attempt to transmit HIV to another individual.