Unlawful Turn-Aways Act of 2021 This bill addresses training for Department of Veterans Affairs (VA) employees regarding discharge eligibility standards for VA benefits and services, requires notification of eligibility for VA benefits and services for individuals who were discharged or released from active service under conditions characterized as neither honorable nor dishonorable, and modifies the requirements of eligibility for certain mental and behavioral health care related to military sexual trauma, readjustment counseling, and related mental health services.