Essential Caregivers Act of 2021 This bill requires skilled nursing facilities, nursing facilities, intermediate care facilities for the intellectually disabled, and nearby inpatient rehabilitation facilities to establish an essential caregivers program during a public health emergency. Under the program, facilities must allow each resident to select up to two essential caregivers to provide daily living assistance, emotional support, or companionship during the emergency. Facilities must afford such caregivers 12 hours of access to residents each day (or unlimited access for end-of-life care), and caregivers must agree to follow facility protocols for staff safety. Facilities may deny access to caregivers who violate protocols, subject to certain notification requirements; the Centers for Medicare & Medicaid Services must establish an appeals process relating to such decisions and may take specified enforcement actions against facilities that violate the bill's requirements.