I would allow one child for this reason. If they say it's for personal beliefs or their fear of autism, I would not take the child. Because if they can't listen to facts from medical professionals, they probably won't listen to me either!
This is why I personally think it best to not get into the reasons why a parent has chosen for or against vaccinations. What one person holds as true, may in fact be false and that applies to all of us. Values, medical facts etc etc Fear of autism is a valid fear backed up by medical research. What information one person has gathered may be very different than another's. For every piece of fact saying one thing, there is another saying the opposite. If a provider isn't comfortable with it one way or another then it should be as simple as that not needing an explanation from a parent because regardless of how valid or invalid their reasoning, it should have no impact on your vaccination policy for enrollment. An unvaccinated child is exactly that regardless of the reason why and if your policy does not accept then it doesn't accept.