Achieving Racial and Ethnic Equity in Disaster Response, Recovery, and Resilience Act of 2020 This bill establishes the Office of Equal Rights and Community Inclusion (OERCI) within the Federal Emergency Management Agency (FEMA). The OERCI shall be responsible, among other things, for (1) improving underserved community access to disaster assistance and improving the quality of assistance such communities receive; and (2) eliminating racial, ethnic, and other underserved community disparities in the delivery of various preparedness, response, and recovery assistance. The bill defines underserved community to mean an historically disadvantaged community, including the Native American, African-American, Asian, Hispanic, Pacific Islander, Middle Eastern and North African, rural, low-income, and disability communities. FEMA shall (1) administer and evaluate its programs and activities, including those of recipients of preparedness, response, recovery, and mitigation grants, in a manner to affirmatively further inclusion and engagement of underserved communities and improved outcomes for underserved communities tied to FEMA programs and activities; and (2) establish an underserved community initiative to award grants to specified nonprofit entities. The OERCI shall develop measures to evaluate the effectiveness of the activities of program offices in FEMA and the activities of recipients aimed at reducing disparities in the services provided to underserved communities. During the period of time for which there is a major disaster or emergency declared by the President with respect to COVID-19 (i.e., coronavirus disease 2019), the OERCI shall regularly consult with state, local, territorial, and tribal government officials and community-based organizations from underserved communities that it identifies as disproportionately impacted by COVID-19.