I don’t think there are any Rabbonim that oppose vaccinations. What I have seen are Rabbonim that hold that you are not required to vaccinate.
My guess is that these are cases where the Rabbi in question is friends with an anti-vaxx doctor who tells him that vaccines aren’t necessary or cause autism or whatnot. The Rabbi then says to himself: if there are some doctors that say it is not medically necessary than I cannot say that it is required and schools should take in unvaccinated children.