Menstrual Equity For All Act of 2021 This bill expands access to free sanitary napkins and tampons (i.e., menstrual products) in certain locations and for particular groups. It also requires Medicaid to cover menstrual products, as well as liners, cups, and similar items used by individuals with respect to menstruation. Specifically, the bill imposes requirements to make free menstrual products available in federal and state correctional facilities (including facilities that house aliens detained by the Department of Homeland Security) and restrooms in federal buildings that are open to the public. It also establishes a demonstration grant program to support the provision of free menstrual products on campuses of institutions of higher education and permits elementary and secondary schools to use certain grants to provide menstrual products to students. Furthermore, the bill requires employers with at least 100 employees to provide free menstrual products for employees. It also permits the use of certain grants for emergency food and shelter to provide menstrual products to homeless individuals.