I thought all anti-vaxxers were idiots. Then I married one

Sounds like you're conflating a few different things here. I don't know any vegans who are vegan out of fear. Usually it is a question of empathy for animals, or for the health benefits.

That legislation should be coupled with the removal of legal liability for children by parents. It cuts both ways, if parents are unable to make choices for their children (even if they are wrong choices) then they should be absolved of all legal responsibility for said children as they are no longer able to act as the guardian in a manner that they view as the best course of action by their children. I would go further and say all financial responsibility as well. Either we are a society that entrust parents to raise their children or we let the state raise them.

What you propose is legislating the greater body for the unsavory actions of a minority while it is becoming more common with more and more federalization of law it always conflicts with personal freedoms and leads to a less free society for all. Someone would find an action that you do at some point in your life, unsavory and illogical and quite possibly harmful to yourself or others, under what you propose we could just enact legislation for the greater good. This runs contrary to the spirit of the law of the land and ends up somewhere closer to fascism. Please note I am not implying that you are advocating fascism but taking away peoples choice to self determination even for their children certainly starts to lay the foundation for a very different society.

What you propose is a slippery slope on the path to the state raising children which in my opinion is a far scarier reality. Life involves risk, and sometimes it involves risk for children. I think it is fair to say if one has made a life choice that puts other kids at risk their kid cannot participate in activities that could place other kids at risk but it is a whole different level to mandate that we start making medical decisions for parents. If we do we should legally acknowledge that parents or at least the legal concept of guardianship as we know it no longer exist.

How do you convince your wife when your child gets the disease that vaccination would have protected them against (which is far more likely to happen, and has cost thousands upon thousands of recorded deaths in the past)?

Your question is analogous to: "If you told you kid it's ok to go out and play, and while outside a car hit him, do you let the other child ever go out again?" probability wise.

The author gives a good overview of the psychology of an anti-vaxxer:

1) Anti-vaxxers aren't paranoid misfits TL;DR: Anti-vaxxers are normally rational people, but with an incorrect view on a topic.

2) It's all about fear TL;DR: Anti-vaxxers hold their view out of an irrational fear, similar to arachnophobia, and simply using reason and facts won't work, as they're not in a frame of mind to accept them.

3) If you think something is dangerous, it's logical to avoid it TL;DR: Though their starting premise is misguided, an anti-vaxxer's reaction to vaccines is logical. Thus, there is an emotional component in the initial premise that, when confronted with facts and reason, lead them to dig their heels into the sand and hold the line instead of thinking logically.

4) There's an industry supporting anti-vaxxers — and we're driving them into its arms TL;DR: There are people positioned to exploit fear, and it is these people who are validating the anti-vaccination movement, despite various ethical concerns, and allowing it to thrive. Without these people, the movement would have died out shortly after it had started. Also, anti-vaxxers seeks support from loved ones and people who have experience with the subject matter to validate their worldview.

5) Changing someone's mind doesn't just take love. It takes empathy. TL;DR: Anti-vaxxers come to their erroneous conclusion about vaccinations after bad experiences, not logic. The road to change minds is through empathy, not attack.

He makes an interesting quote in his article: "The anti-vax position was not a deal breaker for me, but suggesting that we should expose her daughter to grave dangers for no good reason was a deal breaker for my wife." This reasoning could (and arguably should) be applied in reverse: suggesting that we should expose children to easily preventable dangers (various potentially lethal childhood illnesses) for no good reason should be a deal breaker in any kind of relationship. While empathy could change an anti-vaxxer's mind, the dangers of having children unvaccinated while this strategy is employed is too risky, so a more direct approach, in my mind, must be taken. It's like trusting someone to drive you to the store while they're very drunk when it's better to never get into the car and to stop them from driving, if possible.

Likewise, he compares the anti-vaxxer movement to arachnophobia. His conclusion to drop his stance on vaccination doesn't logically follow from this comparison, however, as arachnophobia is a mental illness, treated by certified therapists when the phobia starts preventing people from living their lives or driving people to impact other people's lives. The logical conclusion to this comparison is to treat the anti-vaccination movement as a mental illness, encourage anti-vaxxers to seek out certified therapists, and enact laws to prevent people who don't vaccinate their children or themselves from spreading easily preventable but potentially life and quality of life threatening diseases.

>This then leads to the argument that non-experts should respect the scientific consensus, but then how does a non-expert evaluate the credentials of a commentator to determine whether they are in fact an expert and part of a real scientific consensus?

This is an excellent and pertinent point. As the article delved into, a lot of these people are big followers of "alternative medicine", which is a field chock full of con artists and shysters claiming to be "experts". If someone is gullible, then they're easily convinced by these fraudsters that their "treatments" are real and work, even though it's just the placebo effect.

I'm just like the article's author: I was married to someone like this. My advice if you find yourself in a relationship with someone big into anti-vax or alternative medicine: GET OUT. If you have a logical worldview that isn't full of conspiracy theories, and you believe in things supported by real evidence, and your partner doesn't, then the disagreements over this stuff are going to tear your relationship apart. Just the sheer amount of money my wife spent on all that crap was one huge factor in our marriage failing.