Conscience Protection Act of 2021 This bill provides statutory authority for certain protections for health care providers that refuse to participate in abortions based on religious beliefs or other convictions. Health care providers include individual professionals, medical facilities, health insurance organizations, and social services providers that refer clients to health care services. The federal government and entities that receive federal funding for health-related activities, including state and local governments, may not discriminate against a health care provider that refuses to be involved in, or provide coverage for, abortions. Currently, similar requirements apply to various related activities, including certain employment or personnel decisions (the Church Amendments), abortion services training (the Coats-Snowe Amendment), qualified health plans offered through health insurance exchanges, and annual appropriations bills for the Department of Health and Human Services (HHS) and other federal agencies (the Weldon Amendment). The HHS Office for Civil Rights must investigate complaints of this kind of discrimination. Furthermore, HHS may terminate or reduce HHS funding for health-related activities if a person or entity fails to comply with nondiscrimination requirements. Additionally, the Department of Justice or any entity adversely affected by such discrimination may bring a civil action to obtain appropriate relief. A plaintiff does not need to seek or exhaust administrative remedies before bringing the action. A plaintiff may also bring an action, including one for money damages, against a governmental entity. In many cases, principles of sovereign immunity shield states and some localities from these kinds of actions.