Cuban Family Reunification Modernization Act of 2021 or the CFRM Act of 2021 This bill establishes a program to provide immigration parole to eligible Cuban nationals for family reunification purposes. (Parole is official permission to enter and temporarily remain in the United States.) To be eligible for parole under this bill, a Cuban national must be a beneficiary of a petition for a family-sponsored immigration visa. A sponsor may apply for parole for the beneficiary before the beneficiary receives an immigration visa. An eligible beneficiary must meet certain criteria, such as passing a medical examination and background check. An individual who has committed a gross violation of internationally recognized human rights shall not be eligible for parole under this bill. Parole provided under this bill shall be for two years. An individual who receives parole may apply for work authorization. The Department of Homeland Security (DHS) shall take reasonable measures to prioritize the parole applications where the beneficiary is (1) an individual with a terminal illness, or (2) a qualifying minor child (generally a child with a parent with a soon-to-expire immigration visa). DHS may operate an immigration processing facility at the U.S. Naval Station in Guantanamo Bay, Cuba, if the Department of Defense certifies that such a facility would not hinder the station's operations or pose a threat to national security.