If we look at a lot of the modern conspiracy theories (antivax, covid being fake, gun crime against schools being a hoax, global warming being a hoax, etc), they all seem to be things that people feel powerless about.
The four I listed are things individuals can't do much about. And modern society is all about the cult of the individual. It would require large scale collective action to deal with them, and if you reject outright the concept of collective action then the easiest way to cope is to pretend the issues don't exist.
Having vaccine anxiety is distinct here. There, some power does indeed rest with the individual. You can test for hyperactive immune systems and allergies, so can know if a given type of vaccine is safe. And yet people who are anxious aren't obviously getting tested.
Now, some who are aren't getting listened to by doctors, and that's a legitimate complaint. Some of that is because doctors are overworked, and that too is a perfectly legitimate complaint. And there has been (and still is) a lot of sexism and racism in the medical profession, leading to poorer outcomes and unnecessary injury/death.
These issues are verifiable, very real, urgently need to be fixed and should not be accepted by anyone. But that is precisely what makes them different from conspiracy theories. They're trivially verifiable. There are no aliens or crime syndicates hiding this information.
There are other conspiracy theories, such as the tendencies of politicians and the powerful, whether Lord Lucan is alive, a new world order, and so on.
These also look like a feeling of being powerless, and a way to "explain" why the person is powerless. After all, if politicians are alien lizards or part of an organized crime syndicate, then the public would obviously be powerless. That would be a natural conclusion.
The last category, what might be called traditional conspiracy theories, would be the flat Earth movement, the fake moon landings belief, and so on.
The idea here seems to be, again, powerlessness., this time based on the notion that the public isn't being told everything, that scientists are keeping secrets.
I can understand that to some extent. Governments are loathe to let scientists talk freely, it's natural to be suspicious about things you're not told and the paranoia over secrecy extends to things that the public already know.
(Strong encryption exports were only legalised in the US after one person had the RSA algorithm tattooed onto him.)
Extrapolating from this paranoia to the idea that the moon is a hologram is a stretch, but it's understandable that some people will react badly to this feeling of powerlessness and helplessness, and unelected scientists are easy, soft, targets.
All of the above also involve this idea of having secret inside knowlegde about "the truth" (which is also about control, since now you get to be the one who controls it).
Since the underlying issues revolve around the worship of the individual over all else (and thus making personal power sacrosanct and all that denies such power a heresy), maybe one step would be to have schools teach a more balanced approach rather than reinforcing this absolute ideal.
Extremes (be it a communal extreme, an individualist extreme, a hedonistic extreme or an ascetic extreme) are toxic but modern discourse doesn't leave any room for the middle ground any more.
And when that middle ground is claimed, it needs to be claimed by all sides. The extreme position, I suspect, is a reflex reaction of all the other extremes.
The second part is about control issues. Everyone wants to be the leader, nobody likes following, and in a world that respects status and glamour rather than people, there's an obvious reason for that. Control is also a mental health issue and in the whole strong, self-sufficient ideology, mental health issues are something only other people have.
Banish the extremes and the glorification of indvidualism and power. Science isn't the problem, nature is never a problem, and even politicians don't have to be a problem if they don't want to be.
Then we can finally start seeing rational debates and actual solutions to problems.