Restoring Normalcy in America Act This bill provides civil rights and employment protections for individuals based on their refusal to receive a COVID-19 vaccine and addresses other matters concerning the COVID-19 pandemic. Specifically, the bill prohibits discrimination in places of public accommodation and in federally assisted programs based on an individual's COVID-19 vaccine refusal. In addition, the bill prohibits employers from discriminating against such individuals, including discrimination related to hiring, compensation, advancement, or other employment opportunities. Further, the bill makes it unlawful for an employer to fail to offer any employee who was discharged for a COVID-19 vaccine refusal a position at an equal level and rate of pay to the position the employee held prior to discharge. In particular, the bill provides for the reinstatement of any member of the Armed Forces or federal employee who was involuntarily separated because of a COVID-19 vaccine refusal at the request of an affected individual. Any adverse action related to a COVID-19 vaccine refusal must be removed from an affected individual's military record or personnel file. Additionally, the bill (1) terminates the authority of the Food and Drug Administration to authorize under emergency procedures any drugs, biological products, or devices to prevent or treat COVID-19; and (2) requires the Department of Health and Human Services to study the effectiveness of COVID-19 vaccines and treatments, preparedness for future pandemics, and related matters. The Government Accountability Office must also audit certain federal funding for COVID-19 activities and programs.