The analogy is faulty.
The true analogy would be that one feels the government has no right to tell you that you have to feed your kids meat because your research shows that eating meat carries risk with it (heart disease, obesity, etc) even though it is of benefit to a great majority.
I'm pro-vaxx but also pro-choice in this regard. I believe in the science of vaccines, have them myself, and had I children would get them for them. But I also believe that the government should have no say in what I do, or don't, put in my body. Now, the government does have a say in who can be in public property and thus they have a right to state that only vaccinated individuals can be around public buildings or schools... part of pro-choice in this context is that we also have a choice of who we hang around with.
So while I support voluntary vaccination, I cannot support state-mandated vaccination... i cannot support the government telling me what I should, or should not, put into my body.
I know someone who got the flu shot and was in a car accident two days later. The dangers are REAL!
On a serious note, I recall reading the account of a woman who was in the waiting room to have her child vaccinated when the infant had a seizure. If that seizure had happened 30 minutes later, there's nothing on Earth that would have convinced the woman it wasn't due to the vaccine.