Earlier quoted context omitted.
Companies can mandate no smoking as a condition for entering their buildings. Is this also an example of the company having an unreasonable say in what happens with your body?
I wouldn't compare a vaccine to a no smoking rule, it's not the same.
Whether it's mandating what goes into your body or what doesn't, the aim of the policy is the same: Preventing the reckless behavior of one person from harming other employees.
EDIT because I can't reply:
I don't understand what you mean by "give up control of your body". There is no evidence that taking a COVID vaccine results in loss of control of your body or limbs, or remote control of it by someone else. Hundreds of millions of people have taken it, and they all remain fully in control of their bodies.