Mental Health Equity Act of 2020 This bill establishes programs to address racial and ethnic mental health disparities. Specifically, the Substance Abuse and Mental Health Services Administration must award grants that address racial and ethnic health disparities by (1) providing integrated health care in areas with a high proportion of racial and ethnic minority groups, and (2) developing national programs for health professionals to reduce such disparities. The bill also (1) reauthorizes the minority fellowship program to support the education of mental health professionals who provide services to racial and ethnic minorities, (2) requires a study on mental health disparities and a commission on the effects of social media use on adolescents, and (3) prohibits the use of federal funds for specified conversion therapy in the context of sexual orientation or sexual identity.