I know this may seem like an extreme view

I'm not sure it is, lol. I'm not going to defend or condonce antivaxxing, but home schooling would be problematic.

The whole underlying problem with antivaxxers is ignorance, for which the absolute best remedy is education. Denying these kids education would effectively only make them more ignorant. School and social places like it are also really important for developing social skills.
Forcing the kids to stay home would lead to their problems stacking over the course of generations, only making the underlying problems worse. Those same underlying problems also drive poverty, unemployment, crime, etc. We need more kids getting a proper education, not less.

As for letting unvaccinated kids go to school/parks etc. Never in a million years. Nobodys google-fu doctorate is worth an innocent child's life, much less one that isn't theirs. They can build private schools and parks just for themselves for all I care. I don't see how they trust schools anyway since they don't trust the doctors they produce, so it shouldn't be a problem.

My suggestion is this: Slap every parent that denies their kids vaccinations with a gross negligence and child abuse and lock them up. If you're willing to destroy an innocent child's life, I don't see why you deserve one. Foster the kids and vaccinate them. Foster care isn't exactly a great thing for the child either, but it beats having a parent that is trying to kill you. If your child has diabetes and you refuse to medicate, the kids will be fostered to protect them. How this is supposed to be any different is beyond me.