Conscience Protection Act of 2019 This bill provides statutory authority for certain restrictions prohibiting discrimination against health care providers that refuse to perform abortions. Specifically, the bill prohibits the federal government, as well as state and local governments that receive federal financial assistance for health-related activities, from penalizing or discriminating against a health care provider based on the provider's refusal to be involved in, or provide coverage for, abortions. Currently, similar provider nondiscrimination requirements apply to certain employment or personnel decisions (the Church Amendments), abortion services training (the Coats-Snowe Amendment), and qualified health plans offered through health insurance exchanges. Annual appropriations bills for the Department of Health and Human Services (HHS) and other federal agencies have also included similar language (the Weldon Amendment). The HHS Office for Civil Rights, in coordination with the Department of Justice (DOJ), must investigate complaints alleging discrimination based on an individual's religious belief, moral conviction, or refusal to be involved in an abortion. DOJ or any entity adversely affected by such discrimination may obtain equitable or legal relief in a civil action. Administrative remedies do not need to be sought or exhausted prior to commencing an action or granting relief. Such an action may be brought against a governmental entity and may include money damages against such entity.