Nobody is coercing you to do anything when your employer doesn't want people spreading disease in their company. Nobody is coercing anyone if e.g. hospitals refuse to hire someone who hasn't had certain vaccinations. It has nothing to do with coercion. It has to do with the fact that actions and choices have consequences. You don't get to willingly disregard (the safety of) everyone else and expect to be welcome everywhere.

If I choose not to shower, and stink to high heaven, some employers won't hire me. If I choose not to wear shoes, or walk around in my underwear, I will be denied access to many places. Does this mean I am being coerced to shower and wear clothes?

Actions have consequences. It's just that simple. You can always choose to not do x, but when it's a requirement for y, you won't get to do y unless you do x. And speaking of rights, what about everyone else's rights to not have to sit/work/eat/wait next to Typhoid Mary? Or is it really your opinion that whatever someone does, their right to do whatever is more important than the rest of society? Do you think businesses should be forced to allow anyone inside no matter what? Employers are not allowed to set requirements for their employees?