The only positive for me from this misinformation plague is that as soon as the next issue comes along all of the anti-Covid vaccine sentiment will be completely forgotten.
Don't believe me? When was the last time you heard about the MMR vaccine causing autism?
The "good" part of this is that rejection of science, politicization of science and the use of this issue to manipulate people who somehow claim to be "free" yet are the most easily manipulated aren't new issues. There was the MMR autism issue, resistance to polio vaccination and resistance to smallpox vaccines before that.
The damage is of course huge. The US is sitting at >3,500 Covid deaths per day currently. Annualized this is well over 1 million people per year (although it'll likely trail off), 90-95% of whom are now unvaccinated. These are people who are now steadfastly choosing to die. The government has moved on from this (eg the updated CDC guidelines on isolation to keep the economy going). People seem to have moved on (IME).
I don't think we should be worried about censorship of misinformation. Credible-sounding misinformation is easy to produce and hard to refute (aka the bullshit asymmetry principle). Leaving it out there does more harm than good (IMHO). You'll never completely get rid of it but the less of it out there the better.
As to what to do about this, the only cure is to teach critical thinking at a relatively young age so people can ask questions like "who is telling me this?", "what are their sources?", "why shouldn't I trust the CDC?" and "who benefits from me believing this?". Conservatives know this which is why they're busy passing laws to prevent such teaching.
It's why college graduates tend to be more liberal: colleges generally teach critical thinking and that tends to kill conservatism. Of course this is predictably painted as colleges being hotbeds of political indoctrination. So here we are.
A big problem with misinformation being out there is how people can fall into the trap of bothsidsing the issue (which is a logical fallacy, for the record).