Both the Pfizer and Moderna mRNA vaccines have been granted an emergency use authorization by the FDA, not a license. Both vaccines are essentially still in the testing phase, as this article points out, only now the general public is a part of that test, the results of which will not be known for several years.
As more employers ignorantly make COVID-19 vaccination a condition for continued employment, we’ll see a flood of costly litigation that will affirm these federal protections.