End Diaper Need Act of 2021 This bill establishes and expands programs to increase access to diapers and related supplies primarily for low-income families. The Department of Health and Human Services must award demonstration grants to entities with experience in community distribution of basic necessities or other community services to meet diapering needs of eligible families with infants and toddlers. Additionally, the bill permits states to use Medicaid funds to provide medically necessary diapers and supplies to certain low-income families. These families must have a child who is over age three and diagnosed with a serious condition such as bowel or bladder incontinence. 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.