End Diaper Need Act of 2021 This bill establishes and expands programs to provide low-income families and other vulnerable groups with access to diapers and related supplies. Specifically, it provides additional funding for FY2022-FY2025 to meet the diapering needs of certain low-income families and adults through the Social Services Block Grant Program. This grant program provides a flexible funding stream to states and territories to support social services for vulnerable children, adults, and families. The bill exempts these funds from sequestration. Sequestration is a process of automatic, across-the-board reductions under which budgetary resources are permanently cancelled to enforce specific budget policy goals. In particular, these funds must be used to meet the diapering needs of low-income families with one or more infants, toddlers, or medically complex children (i.e., children who are age three or older and diagnosed with a serious condition such as bowel or bladder incontinence); and low-income adults and adults with disabilities who rely on diapers and other adult incontinence materials. Additionally, the bill permits states to use Medicaid funds to provide medically necessary diapers and supplies to low-income families with one or more medically complex children. It also allows individuals to buy medically necessary diapers and supplies with funds from health savings accounts and other tax-advantaged accounts for health care expenses.