Removing Environmental Hazards And Building Safely Act of 2021 or the REHABS Act of 2021 This bill authorizes the Department of Housing and Urban Development (HUD) to award grants to national and regional organizations and consortia to abate and remove environmental hazards (e.g., lead, asbestos, and mold) in homes being rehabilitated for families and individuals who otherwise would be unable to afford to purchase a dwelling. Additionally, HUD must study the assessment and removal of mold in the rehabilitation of a single-family home.