Department of Defense Anti-Semitism and Racism Awareness Act of 2020 This bill directs the Department of Defense (DOD) to include in its surveys questions regarding whether respondents have ever (1) experienced or witnessed racist, anti-Semitic, or supremacist (or extremist as under current law) activity in the workplace; or (2) reported such activity. DOD must submit to Congress a report including (1) the text of the questions included in surveys, and (2) which surveys include such questions.