When an anti-vaxxer insists on not having their children vaccinated, it raises ethical issues on multiple levels. First, the parent violates their duty towards their children, which undoubtedly includes medical care. Second, duties aside, the parent violates the child's right to life by intervening in their reception of standard medical treatment. Third, the parent violates other children's right to life by rendering their child susceptible to contagious diseases that may then transmit to other children.
I have long struggled with the ethicality of letting parents have control over how they raise their children. After all, most parents do one thing or another that is harmful for their children. But at what point is it the state's responsibility to step in? Surely when there is apparent abuse. Maybe not so surely when there's withholding of vaccination. So where does one draw the line? Parents who take their kids to fast food restaurants every day, which would lead to a dangerously unhealthy lifestyle, obesity, and eventually an earlier death? Parents who send their kids to cram schools 20 hours a week, making them grow up devoid of dreams?
That's why the line is drawn not at the first ethical violation I mentioned, or the second. It's drawn at the third, where the parent risks the lives of everyone else in the community. But as much as I want to propose that unvaccinated people be restricted access to public facilities, that seems to punish the child more than the parent.
To me, it seems apparent that every parent should vaccinate their children. But that's not the real question here. The real questions are much more slippery.