An obvious point, but not one I had seen people making:
The only way to address these fundamental conflicts is to take the State out of the equation. Let private property owners set the relevant rules on their land. Privately run schools, daycare centers, youth clubs, and pediatricians can set their individual policies regarding vaccination requirements for participating children. Health insurance companies can decide if they will insist on vaccination in order for a newborn to remain on a parent’s plan.
Private property doesn’t eliminate conflict, but it is a necessary foundation for the peaceful resolution of very heated disagreements. Bringing the State into the picture will hurt all children.