I still don't understand your stance. Surely the public isn't barred from engaging in the scientific conversation if they have anything meaningful to say. It's just that that conversation is not very accessible because it is so technical. That was also the case in the Enlightenment: Science was practiced by those who had the time and resources to contribute substantiative knowledge. Speaking in broad strokes, the anti-vax movement strikes me as a counter-cultural movement, an "outsider art" to the mainstream scientific conversation. It's not that they can't engage with the science, it's that they reject that conversation altogether.