In the many, many, many discussions I've had with serious anti-vaxxers, it boils down in every single case to someone's mother being unvaccinated and their exposure to the Wakefield propagandists, combined with a selfish desire to exercise control the child. In many cases, there's also an immense desire to go against any authority figures.
I'm sorry to state it as baldly as that, but it's been my experience, with around thirty or so people, both face-to-face and online. Only one protagonist was male.
There are at least two significant issues with trying to address their concerns. First, the number of hoax or ignorant videos and websites pushing the anti-vax agenda outnumbers genuinely helpful sites 10 or 15 to 1. Any pro-vax YouTube video will also have at least a dozen anti-vax videos advertised.
Secondly, the honestly of our spokespeople works against the almost non-existent medical comprehension of all anti-vax parents. Any words like 'rarely', 'safe', 'unlikely', 'almost', and other weasel words are seized on and used as escape clauses. Since we can't ethically just say '100% safe', we need to educate the parents individually. We need great analogies that make sense to them, not statistics! Trust me - most of these parents understand statistics less than medicine, and they don't understand that at all, for the most part.
I've actually seen a vaccine described as (and I quote) : bits of aborted fetus, soaking in mercury, and corrupted with preservatives. No, I'm not kidding.
Even the herd immunity argument works against us - they hear the word "herd" and think you're INSULTING them! That could do with some marketing speak!
And unfortunately, a very seriously deluded woman is currently suing her husband for vaccinating their children behind her back! It won't get past the first hearing with any luck. But I've already seen the anti-vax propaganda machine telling people that, if the hearing rejects the suit, it's because the judge is controlled by 'big pharma'!
There's a huge industry dedicated to stopping all vaccinations, but I don't understand how they benefit from their stupidity. It has to be money... the only thing I can think of is that there's a corporation funding them, in an effort to get the government to privatise the vaccine industry, and then dig into the lucrative market once people start getting more scared of the disease outbreaks than they are of vaccinations. Crazy, I know.
I'm sorry this doesn't help the OP, but maybe it might be food for thought...