siamesecat: I think that there are valid reasons to consider some penalty for not vaccinating, yep. Mass innoculation is what makes it effective - people not getting vaccinated poses a real threat to the rest of us.
As for how much control parents have over their children? Enough!
If your child is sick and won’t get help, we have a medical and legal system that addresses that. If the issue was the child not wanting medical treatment, that is a slightly different issue but the system can only handle cases that it is aware of. (And, admittedly, sometimes not all that well!) An intentionally mis-informed child is in no position to make life-affecting decisions.
This is not a slipperly slope - a consenting adult choosing to ignore proven medical intervention is welcome to do so as long as the ill effects that they will face will be theirs alone. Someone who is extremely contagious that wishes not to be treated will be (and this happens) detained for the safety of others. However, if someone wishes to let cancer overtake their body and not go through radiation or the like, the legal system accepts that.
Forcing (either by not allowing them or by teaching them that they will go to hell for doing so) a child to not get medical help for a treatable illness (or any illness for that matter) is not acceptable.
With regards to teaching your kids that gays will go to hell or teaching them to be Nazis - it is wrong to do both or either. Children should not be indoctrinated into a faith and they should not be taught to hate.
If it is religion that causes a person to not seek solutions to their problems, it is another black eye for something that has never given itself a chance for the initial bruising to subside.