If he's sick, you do not broadcast his mental illness out of decency and respect. That's not the interesting thought experiment. The interesting one is broadcasting true believers in their right minds.

In those cases, you make the best argument possible to refute that drinking bleach us harmful... which honestly isn't that hard to make. The hard part is building up a reputation as being someone respectable and respectful enough to deserve attention. I think that silencing of sincerely held beliefs undermines efforts to actually persuade, inform, and make progress (and peace!).