No Asylum for Criminals Act of 2021 This bill bars an individual who has been convicted of a crime from receiving asylum, with limited exceptions. Specifically, the Department of Homeland Security may designate political offenses committed outside of the United States that shall not be considered a crime for this purpose. Currently, an individual shall be barred from receiving asylum for only certain types of criminal convictions, such as if the individual is convicted for (1) an aggravated felony, or (2) a particularly serious crime and as a result deemed a danger to the United States.