Fairness for Rural Medicare Beneficiaries Act of 2021 This bill modifies the payment methodology and coinsurance amount for outpatient critical access hospital services under Medicare. Currently, the payment rate for such services is 101% of reasonable costs; the coinsurance amount for such services is 20% of the applicable charges. The bill modifies this methodology so as to base the 20% coinsurance amount on the fee schedule under the Medicare outpatient prospective payment system.