Is it true that households have to complete the 2020 Census in order to receive the “stimulus” checks that may be mailed to households by the federal government as a response to the financial impacts of the COVID-19 pandemic?

No. The two processes are completely separate. The information that you provide concerning your household for the 2020 Census, including whether or not your household responded at all, is kept completely confidential. As a result, the federal government would not be able to condition issuance of these checks on completion of the 2020 Census.