Having the vaccine... might give you a sore arm for a bit.
There are Lot of MNers hysterically reporting stronger reactions than that.
Thing is, that argument isn't about bodily autonomy... it's about harms & benefits. Most of the counter-arguments given here against vacc mandates are not addressing bodily autonomy. Instead they are insisting that other principles are more important than bodily autonomy.
That is pretty much what the pro-life brigade say about abortion. That bodily autonomy is secondary to other moral principles, and that the most sacred of these is Right to Life (of the embryo/fetus). So you agree that other things matter more than bodily autonomy.
Nearly All of you saying "It's not the same" are agreeing with OP -- you may not realise it. You don't support bodily autonomy when it comes to Covid vaccines, you are arguing that other things matter more than bodily autonomy.
I dunno if bodily autonomy is "the most important principle" but once you start downgrading it you should not be surprised how much others downgrade it, too.