Vaccine mandates are already ubiquitous across the Western world (and the non-Western world). In most cases, it is infants and children having a "medical procedure" forced on them. Your point still stands, but in reality an overwhelming consensus exists that vaccines are an acceptable exemption to bodily autonomy.
EDIT: I didn't make an argument, I only stated uncontroversial facts. Would love an explanation of downvotes.
In practice, yes. It is codified into law in countless nations and there are no major movements to change those laws. So in terms of the reality of being a living human being in any given society (free or not), yes, bodily autonomy is limited by many, many things by the state, one of those being vaccine mandates. You may not like it, but that is simply the reality.
EDIT: I didn't make an argument, I only stated uncontroversial facts. Would love an explanation of downvotes.