Family Unity Act of 2021 This bill modifies the scope of a statutory prohibition against the judicial review of claims involving the removal of a non-U.S. national ( alien under federal law). Currently, a court is barred from reviewing any claim by a non-U.S. national arising from a decision by the Department of Justice (DOJ) to commence proceedings, adjudicate cases, or execute removal orders against a non-U.S. national. Under this bill, a court is only barred from reviewing a claim by a non-U.S. national challenging a discretionary decision by DOJ to take such actions.