As far as I'm concerned, NO employer has a right to force employees to accept anything into their bodies without a pre-existing contract signed at the time of hire.
In the 1950's and 1960's, it could be reasonably trusted that vaccines were safe and devoid of unknown additives. Today, there is CONSIDERABLE doubt. For instance, today, tetanus vaccines have whooping cough vaccines added and you have no choice in the matter. What is being added to the flu vaccine without your knowledge? Who knows? If somebody guarantees you that nothing has been added, do you trust him/her? My sphere of trust has diminished tremendously in the last five years.