They both said they feel immense pressure not to speak out against the vaccine or publish anything against it. So the regular channels of dissent have been removed.
If they had significant data a journal would pick them up. There is no one silencing them but themselves, because they know they don't have good evidence and their sources also don't have good evidence. The lancet, one of the most prestigious journals in the world, took up an article that vaccines might be related to autism, because at the time the authors had significant data (that later turned out to be fraudulent but at this point pandoras box had already been opened, and now decades later people believe vaccines cause autism). So if they did have this smoking gun data that said the vaccines are something to be worried about, it would have been published by now in a huge journal.
Great points. In particular, that one original source of anti-vax anxiety comes from a study published in a top medical journal. If one thinks that the medical establishment is corrupt or self-censoring, or should not be trusted, etc., then does that also not apply to articles published in The Lancet?