COVID-19 Nursing Home Protection Act of 2021 This bill provides funds and establishes requirements for Medicare skilled nursing facilities (SNFs) and Medicaid nursing facilities (NFs) to address COVID-19 (i.e., coronavirus disease 2019). Specifically, the bill provides FY2021 funding for COVID-19 strike teams that can be deployed to these facilities to help with vaccinations, clinical care, infection control, or staffing. The amounts provided by the bill are designated as an emergency requirement pursuant to the Statutory Pay-As-You-Go Act of 2010 (PAYGO) and the Senate PAYGO rule. (This excludes the budget effects from being counted for the purposes of enforcing the PAYGO rules.) In addition, the bill requires the Centers for Medicare & Medicaid Services (CMS) to ensure that, during the public health emergency relating to COVID-19, at least one of its contracts with Medicare quality improvement organizations requires that the organization assist SNFs with COVID-19 infection control (e.g., training materials). Finally, the bill provides statutory authority for the requirement that SNFs and NFs report data regarding COVID-19 preparedness, testing, infections, and deaths. Additionally, the CMS must publish on the Nursing Home Compare website certain demographic information, aggregated by state, with respect to COVID-19 infections and deaths in such facilities.