If person A's lies have clearly and demonstrably hurt person B's reputation, relationships, livelihood, and personal safety, should they have any recourse?
I wonder if a good modern analogy for Semmelweis would be if we did a study on crystal healing or Reiki, and the crystal healing/Reiki was found to vastly outperform placebo pills. (Actually something like this sort of did happen with parapsychology. The effect sizes were pretty small I believe, though.)
Obviously in hindsight, other docs still should've listened to Semmelweis. What I'm trying to get at here is that sussing out the truth can actually be a pretty tricky thing. Even if the docs had somewhat good reason to accuse Semmelweis of spreading medical misinfo, it was still a catastrophic mistake in retrospect.
I don't necessarily mean to indict the scientists of Semmelweis's day too much. I mean, they fucked up, to be sure. However it's understandable (somewhat) why they didn't listen to him.
But a society that allows those presently in power to censor information they consider to be false is a society that helps cement its present ways of doing things for eternity. I don't think that's a good thing.
A modern example of this might be the plaque theory of Alzheimer's disease. I don't know enough to know whether this is a fair description of the state of the science, but there is certainly a growing view that, a "cabal" of believers in this theory suppressed alternative views for a long time. It may end up being that the cabal is right! But it seems to me like there's enough uncertainty that a diversity of viewpoints should probably be heard.
One indicator of the quality (or lack thereof) of a society is how easy is to damage one's reputation without evidence. That's why the whole "Believe women" movement is complete and utter bullshit.
This problem has always existed, and the social standing of person A and the social standing of person B typically determined the outcome. Platforms such as Twitter where an unfounded claim can be spread so rapidly and to such a vast number of people are also a modern thing. There's no easy answer, but having the state as arbiter of truth is never the solution.