Resident Physician Shortage Reduction Act of 2021 This bill increases the number of residency positions eligible for graduate medical education payments under Medicare for qualifying hospitals, including hospitals in rural areas and health professional shortage areas. Current law provides for an increase of up to 200 positions per fiscal year beginning in FY2023, with a total increase of 1,000 positions; each hospital may receive up to 25 additional positions. The bill provides for an additional increase of 2,000 positions per fiscal year from FY2023-FY2029; during this period, each hospital may receive up to 75 additional positions in total under the bill and current law. Additionally, one-third of the positions that are made available under the bill must be allocated to hospitals that are already operating above applicable resident limits. The bill also requires the Government Accountability Office to report on strategies to increase the diversity of the health professional workforce, including with respect to representation from rural, low-income, and minority communities.