If you treat people like adults and let them consult their doctors and make their own decisions, the bar is much lower for safety (by lower I mean from impossibly high to reasonable). People willingly take much more risky medicines and treatments all the time and are fine with it. But if you try and force something in them, it's not surprising they push back on anything that isn't guaranteed to be perfect.
(So my point is, I think demand would be higher and concerns lower if you just made it available and let people make their own choice. But the whole pandemic has been more about forcing people to do things than about trying to do things that actually solve the problem)
[Edit- it's funny how any presence of giving people control over their bodies evaporates in a situation like this. And re the strawman that "nobody is forcing you" - if the consequence is severe limits on what you are allowed to do, that doesnt really hold up]