The anti-vaxxers send death threats to people who correct their erroneous claims. That's how you shut down reasoned discourse -- by having fervent zealots attack anyone who contradicts them.
Obviously attacking people who disagree with you is the opposite of them having free speech. It suppresses the speech of anyone not willing to be subject to the threats and allows the erroneous information to proliferate unchallenged.
So the problem isn't that the anti-vaxxers got to speak their piece, it's that they're caught up in a subculture that suppresses dissent. Then their subculture declares that two times two equals six and anybody who tries to show otherwise is attacked, which deprives them of reasoned debate as a method for correcting misconceptions, and so the misconceptions persist.