[wizzwizz4]

The only thing that'll convince those people is for authority figures to become trustworthy.¹ I don't see that happening any time soon.

So who're left? The people who are concerned about vaccines because other people are, rather than because of (misplaced in this instance, but not in general) scepticism of the claims of untrustworthy, powerful people. Those people can be reassured by thought experiments, because they're assuming dangers due to incompetence moreso than malice.

¹: I suppose an argument from game theory might, but only if they think the vaccine-poisoning enemy is in it for the long run, so the threat of the truth coming out in (e.g.) 20 years would be enough to dissuade them from something like that. If they think the enemy's plans are shorter-term, or they can afford the loss of face, I don't think there's any way to convince them short of convincing them that the industry behind “non-addictive” heroin, thalidomide (developed by a Nazi war criminal!!) and the contaminated blood scandal is totally cool and in no way out to get you.