Compact Impact Fairness Act of 2021 This bill expands the eligibility of citizens of the Freely Associated States lawfully residing in the United States for certain federal public benefits. Currently, citizens of the Freely Associated States (Micronesia, the Marshall Islands, and Palau) may live, study, and work in the United States as nonimmigrants. However, such individuals are generally ineligible for most federal public benefits, with Medicaid being one exception. Under this bill, such individuals may be eligible for certain federal public benefits, such as benefits under the Temporary Assistance for Needy Families program. Furthermore, current law generally bars individuals from receiving federal means-tested public benefits for the five-year period starting from the individual's entry into the United States. Under this bill, citizens of the Freely Associated States living in the United States shall not be subject to this bar.