Relief for Rural Providers During Emergencies Act This bill waives several requirements and establishes certain minimum funding for rural health care providers during the public health emergency relating to COVID-19 (i.e., coronavirus disease 2019). Among other things, the bill maintains a provider's eligibility to participate in the 340B drug pricing program (i.e., a program that allows providers to receive covered outpatient drugs at reduced prices from manufacturers) for the duration of the public health emergency if the provider was already participating before the emergency began. The bill also requires the Centers for Medicare & Medicaid Services to temporarily waive specified requirements for Medicare and Medicaid providers and services, including certain criteria for critical access hospital certification and coverage of post-hospital care in skilled nursing facilities. Additionally, the bill retroactively requires that at least 20% of appropriations to the Public Health and Social Services Emergency Fund under the Coronavirus Aid, Relief, and Economic Security (CARES) Act relating to COVID-19 provider assistance be distributed to rural health care providers.