The enlightenment involved the promotion of knowledge not "expert", it promoted the belief that a claim should be proven with data, it promoted that the best way to get to the actual truth is with robust inquiry, debate, trial and argumentation
To attempt to equate that with today "The Experts™" and "Authoritative Sources™" who instead of engaging in robust debate want to engage in robust censorship, these "Experts™" and "Authoritative Sources™" are more akin to Dark Ages Priests wanting to burn the heretic than they are of Enlightenment thinkers and scientists
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.