Treating people like children is exactly what many political leaders do to shepherd their own partisans into continuing to support them and it often works. Fearmongering, lies, emotions. Telling them they need you to protect them.
And are we pretending that the anti-vax movement is now perfectly transparent with information and acts like it's an adult debate where they simply make reasonable points? That this cause wasn't driven people who came into it already convinced, who never took the hypothesis of "this could be an effective way to vaccines" seriously at all?
Not every vaccine skeptic is spouting "it's going to rewrite your dna" or "they're tracking you with microchips" and "it's the mark of the beast" but the nutjobs are a quite significant fraction and none of them ended up there because they went looking for data on clinical trials and didn't find as much as they wanted to.