Well, it seems like child abuse to me, and it's not even containable - the effects are not limited to their family, but can effect mine as well* . Second, I don't see a way for political resolution here. On political matters there are votes and if my side loses, that's the way it is. Here, the very fact such a movement exists (even if the vast majority is against it and votes against it) puts some immunocompromised people at risk.
* There are religious sects that agree to basically live apart of society - so it wouldn't matter that much to us what they do - but I don't think that's a possible resolution to this issue, not for most anti-vaxxers.
Typically, the resolution is some form of mandating that kids get vaccinated.
However, given that these parents believe that puts their child and themselves at risk, they'd go far to stop it, up to faking vaccinations - at which point any outbreak would "prove" the vaccines are ineffective. So I don't think there's a way of avoiding a confrontation with the movement itself.
I feel like there a tendency to believe that, since censorship is bad, censorship must also be completely ineffective, and we tell stories like "deplatforming is useless" to reinforce that. But I don't think that's a realistic approach. Censorship can and does work, in the right circumstances. Chinese millennials may know that something happened at Tiananmen Square in 1989, but they're fuzzy on the details and inclined to downplay it and keep quiet about it. That's censorship working as intended. Assuming your enemies are incompetent doesn't accomplish anything but a false sense of security.
All of this is still crude - just less crude then outright censhorship - because the deep roots of the movement are too difficult to root out. Ultimately, this movement is suited to the West in our age. First, we demonize Big Everything (sometimes even with reason). Second, most of the people who reject vaccines ultimately prefer a dead child (even someone else's) over an autistic child. This is also pushed hard in our culture. Third, we have this worship of natural everything, even though nature is full of poisons.