Sanctioning and Highlighting Authoritarian Medicine and Eugenics Act of 2021 or the SHAME Act This bill imposes sanctions on individuals and entities responsible for carrying out coercive policies to limit births in China's Xinjiang province. Specifically, the Department of State shall annually report to Congress the identities of any Chinese government official or agency or any member of the Chinese Communist Party that knowingly orders, controls, or routinely carries out such coercive policies in Xinjiang, such as requiring involuntary abortions or mandatory contraception use. The State Department shall also publish a list of the named entities and individuals on its website in English and Mandarin Chinese. The President shall impose property-blocking sanctions on the individuals and entities named in the report, as well as visa-blocking sanctions on the named individuals. An individual or entity that violates, attempts to violate, or conspires to violate the sanctions provided under this bill may be subject to civil and criminal penalties.