This is a common fear. But nobody is really worried that some charismatic guy who believes that aliens are secretly draining humans of their precious bodily fluids is going to take over the world.
Those in power are always concerned about maintaining their power. Somebody who shows up and says, "hey, these people in power are saying things that are not true and are engaging in damaging and dangerous practices," well, it's quite easy to cast that person as a Dangerous Individual Who Is Secretly A Lunatic. Everybody has some nutty idea, so you focus on that nutty idea, and presto, you have a bona fide nutcase who can be shut down for "misinformation".
I get the argument. But the practical working aspect of it is it puts great power into the hands of already powerful people. That's fine, if you want to have a technocratic/political aristocracy. If you do not, then there isn't many other options other than open discourse.