Returning to the original question posed in this thread:
Almost always, gedolim will disapprove of excluding children from a school. Traditionally, Jewish schools always had open admission. This goes back to antiquity. The theoretical basis is that, de facto, that learning Torah is a right not a privilege. When the Baal ha-battim do try to exclude a child, and someone asks the local gadol, the child typically gets unexcluded. The desire of scome schools to be “exclusive” is something we picked up from the goyim in recent years – it is a “hiddush” that should be rejected.
In all fairness, an unvaccinated child is only a threat to other unvaccinated people – so if a parent is worried they should get their child vaccinated. And if you don’t want to keep out the kids of parents you think are nuts – be sure not to ask a shailoh since you probably won’t like the answer.