It's not censorship against stupidity. It's censorship against bullshitters who spread medical misinformation that may put people in danger; factually untenable opinions, expressed in an assertive manner, in a context which seems authoritative to the layperson.
Nobody says the majority is stupid, nor it is relevant. Protecting a minority is as good an excuse as it is protecting the majority, don't you think?
The quality of US public schools can vary immensely, especially for students in poor areas where the community can't put up much money and education budgets are the first thing to be slashed.
Additionally, many states allow outright lies such as creationism or abstinence-only sex ed to be taught - both of this is further evidence that it cannot be assumed automatically that a person educated in the US is well educated.
To make it worse, antivaxxers explicitly mistrust science and only trust the blogs and "mama groups" and other crap. How is anything the government, scientists, the media, anyone supposed to overcome that mistrust?