Censorship is connected to power. Anti-vaxxers are anti-truth, where they stand with regards to power varies. Hence they have to be fought by providing truth. Fighting them using censorship is very dangerous and only will make them feel even more justified in their demented stance.
Fighting them with truth doesn't work either. Just like other crazy people, such as creationists or flat-earthers, the truth they are denying is well established and beyond any reasonable doubt. Attempting to fight them with truth is pointless because they've already decided to close the ears to it and because engaging them in public debate only serves to legitimize them in the eyes of uneducated fence-sitters. Conspiracy theorists just entrench themselves and close the brains when faced with an onslaught of facts and common sense.
For the above reasons I am in favour of denying them air time and denying them the opportunity to debate, as this only spreads the contagion. That doesn't mean a government clampdown, but it does mean that media organisations can avoid promoting the message by pretending it is a reasonable viewpoint.
No society has complete freedom of speech. In the US the first amendment doesn't offer protection for fighting words, speech that leads to illegal actions, obscene speech, kiddie porn, and commercial activities.