There is a plethora of scientific evidence to prove that vaccinations are effective. They aren’t basing their decisions on science or logic.
If your question is what I think it is asking, about proving theologically that vaccines work, they would need to believe that G-d wants them to protect their children with the vaccines. B”H before anyone gets I’ll chas v’shalom with an easily preventable disease.
I think they would need to be open-minded about it. What does it take for a rabbi to change his view?
More information? Conflicting data? Peer or mentoral support? Evidence that the prior thinking failed? A crisis? A wife’s opinion?
It is odd that they are against vaccines when I hear a lot of how Torah can be like medicine to a person’s soul. Sometimes we need to suffer to get to a healthier and higher place. A closer relationship to Hashem.
Maybe it is that they don’t want to put sickness into their bodies? Expose to that element?