Immigrant Witness and Victim Protection Act of 2021 This bill provides protections for certain aliens who are victims of crimes or abuse and addresses related issues. The bill removes various annual numerical limits on (1) U visas, generally for victims of a serious crime and helpful to law enforcement in prosecuting the crime; and (2) Special Immigrant Juvenile visas, generally for minors who have been abused or neglected by a parent. Applicants for certain immigration benefits, including U visas and T visas (generally for victims of severe human trafficking) shall receive work authorization on the date the application is approved or earlier. Removal shall be stayed for an alien with certain pending applications, such as an application for a T, U, or Special Juvenile Immigrant visa or for relief under the Violence Against Women Act. There shall be a presumption against detaining such an alien, which the Department of Homeland Security may rebut by establishing that (1) the alien's appearance at removal proceedings is not reasonably assured, or (2) the alien is a threat to another person or the community. The bill also prohibits making an adverse determination regarding an alien's admissibility or deportability based on information furnished by certain individuals, such as a spouse or parent who has battered the alien. Current law prohibits making an adverse determination using information furnished solely by such an individual. The bill also limits the use and publication of information provided in certain applications, including T, U, and Special Juvenile Immigrant visa applications.