Safely Back to School and Back to Work Act This bill makes multiple changes to federal public health, education, and workforce training programs in order to respond to the COVID-19 (i.e., coronavirus disease 2019) public health emergency. With respect to public health programs, the bill establishes grant programs, provides contracting and other authorities, and directs other activities pertaining to biomedical research and development of vaccines, diagnostic tests, and countermeasures; the administration of the Strategic National Stockpile; public health preparedness and response; and other issues related to COVID-19, such as allowing employers to temporarily offer telehealth benefits to employees who do not otherwise qualify for health benefits and prohibiting the collection or use of genetic material from COVID-19 tests without written, informed consent. With respect to education and certain workforce programs, the bill revises student loan repayment programs, including by consolidating repayment options; allows the Department of Education to waive certain statutory and regulatory requirements for elementary and secondary schools and career, technical, and adult education programs; establishes grant programs concerning child care providers, eligible scholarship-granting organizations, and certain workers impacted by COVID-19; and makes other changes to programs and funding for higher education, elementary and secondary education, and workforce training.