A few exceptions

There are, however, a few notable exceptions to this kind of blanket requirement. If a work force is unionized, the collective bargaining agreement may require negotiating with the union before mandating a vaccine.

Anti-discrimination laws also provide some protections. Under the Americans with Disabilities Act, workers who don't want to be vaccinated for medical reasons are eligible to request an exemption. In this case, an employer would have to provide reasonable accommodation, such as allowing the employee to work remotely. 

Under Title VII of the Civil Rights Act of 1964, if taking the vaccine is a violation of a "sincerely held" religious belief, they, too, would potentially be able to opt out.

Time to join a church.