Essential Transportation Employee Safety Act of 2021 This bill requires the Department of Transportation (DOT) to support the efforts of state and local governments to prioritize COVID-19 (i.e., coronavirus disease 2019) testing of transportation workers who are categorized as essential critical infrastructure workers. Essential critical infrastructure employees include those who work in industries such as medical and health care, telecommunications, information technology systems, defense, food and agriculture, transportation and logistics, energy, water and wastewater, law enforcement, and public works. Additionally, during the COVID-19 pandemic, DOT must require (1) the owners and operators of equipment or facilities used by passenger or freight transportation employers to implement personal protective equipment and disinfection and sanitization procedures; and (2) an air carrier to submit to the Federal Aviation Administration (FAA) a proposal to permit pilots to wear masks or protective face coverings in the flight deck, including a safety risk assessment with respect to such proposal. The bill sets forth requirements for owners or operators who cannot acquire necessary personal protective equipment due to market unavailability. For the duration of the COVID-19 national emergency, the FAA must (1) provide certain employees, including air traffic controllers and airway transportation systems specialists, with personal protective and sanitizing equipment; (2) ensure that air traffic control facilities are cleaned, disinfected, and sanitized frequently; and (3) ensure its contractors provide their employees with personal protective equipment.