This is the tricky problem. Trusting the marketplace of ideas works if everyone who participates is interested in spending the time needed to evaluate claims.
In my experience, possibly the worst thing that was done was labeling people who argued against forced vaccination as anti-vaxxers, no matter whether they were against vaccines or not. That made a large number of reasonable people very hostile, and reasonably so; they were being declared an enemy.
Why do we have so much compassion for people arguing against forced vaccination, and yet so little compassion for people who were scared of an unknown disease and angry that people were pushing back against the best known way to slow or stop the spread?
Why is the burden of rationality on the latter group? Why don’t they get to be hostile?
I encounter normies talking (inaccurately, lack of nuance, etc) about the "vaccines cause autism" meme on a regular basis.
Anti-vax movements have been around for as long as there have been vaccines. The only thing that "solves" this problem is a new disease and vaccines that completely displaces the old.
Think about it: when was the last time, since the pandemic began, that you heard about autism and the MMR vaccine? that began in the late 90s (with no scientific basis I might add) and persisted for decades. Now no one talks about, thinks about or cares about it anymore. It's completely off the radar.
Covid anti-vax movements will meet the exact same fate come the next major vaccine.