Honestly the thing that changed my mind was looking at the impact seatbelt/child seat laws have had.
You can educate people until you're blue in the face and it doesn't work - we are just not built like that. Not for issues like this. The problem is that you can go about everyday life being unvaccinated, or drive around without a seatbelt, for years, decades even, and have absolutely nothing bad happen. The only time something bad will happen is if you have a crash or if you come into contact with an infectious pathogen. Those things are rare - and outweighed by uncountable experiences of not needing the protective thing and having been fine. In general, we (as in, humans) are built to learn from experience, not theory. We can learn from theory of course. And second hand experience - very few people who see the consequences of non-vaccination or not wearing seatbelts would advocate for the safety of not using these things. (That's why PSAs tend to be so shocking/frightening/emotional). And some people are very risk averse and would go for the most protective option anyway just in case. But for the vast majority of people, repeated experience of the non-protective option makes it seem mundane, ordinary, and safe. That is simply how human psychology works and you can't easily change it.
Laws though for this kind of thing do tend to change behaviour. You can have routes out for people who are really genuinely concerned because ultimately the behaviour of a minority doesn't really matter in terms of achieving the overall goal. But the majority of people don't actually feel that strongly either way. Nobody really likes having an injection or taking their child for one. Nobody likes the hassle of car seats. It is slightly less comfortable to wear a seatbelt than not wear one. Without anything saying you HAVE to do these things, a lot of people will simply not bother. But the moment you make it slightly inconvenient not to do them, it starts to change the social/cultural narrative. These days it is just completely normal to wear a seatbelt and you're seen as a bit of an idiot if you don't.
I don't think it's helpful to write off vaccine-hesitant parents as "idiots" or "crazy" - I think it's actually just a really glaring symptom that there is a growing group of people who distrust medicine and authority/government in general, and that is the problem - why don't they trust? Usually because they don't feel listened to. So I think it's hugely important to listen to those groups and understand what their actual gripes are. Not easily debunkable things like ingredients of vaccines because you can argue back and forth all day on that even though the info is clear and easy to find. No, go to the deep root, and you'll find things like sexism, racism, classism and even horrific crimes perpetrated against minority or disadvantaged groups by governments, medical authorities and so on. That's what needs to be addressed. From the everyday (stop dismissing women's health concerns) to the historical (much better acknowledgement of old harms and new systems in place to prevent anything like "cleansing" ever happening ever again) and the future (encourage young people from underrepresented groups to enter medicine and medical research, politics and government). Also proper funding of the NHS would help so that everyone who needs care can access care.