There does seem to be a holier than thou element at play here. If people don't want to get vaccinated, they should have that choice. I know that is not ideal for the rest of us, but we shouldn't shame people for not wanting to take on what they believe to be a serious risk.
Furthermore, if NFL teams don't want their employees around the facility until they are vaccinated, they should have that choice. Also, employees should have a right to challenge any mandate in the court of law. This is, of course, how democracies function.
There are risks associated with vaccines; however, those risks do not scale. Viruses, on the other hand, do scale. There are multiplicative effects caused by those who are not vaccinated, which increases the risk of more infections. Whereas vaccines only carry risk localized to the individual. It is important to remember that vaccines do not prevent transmission, so just being vaccinated does not mean you are not spreading the virus.