Parent says no vaccinations. Child gets no education. Parent educates child themselves. -Is that your assumption? Well what if they don't? Child grows up unable to read, write or add up.
Future for that child without even basic skills? Is it fair to a child to deny them an education - a future, possibly the ability to earn their own living - because of a choice made by their parents at a time when they were totally unable to have any say in that decision even if they were capable of understanding it?
And unless the child is placed under house arrest, they'd be at the park, in the street, playgroups, in their friends houses, etc. So what does denying them an education help with?
I don't think punishing the child for the choice of the parent is ever the right thing to do.