Imho the problem is that plausible but unprovable alternate realities have been gestating and metastasizing on the internet since almost the beginning of the internet, over two decades now. They've become so normalized in so many peoples' minds that it's now a very difficult problem to even understand, much less address. The possibly-true but not disprovable/unfalsifiable aspect is the hardest part.
There is a mix of motives to these memes. Some of this is being done deliberately, strategically, skillfully in a long-game by entities that have an interest in undermining democratic civil society and with it, democratic government. Others are doing it to advance the interest of particular western political parties themselves, or to advance commercial interests, others just randomly or for kicks and giggles, and some are just true.
It's often difficult or impossible to discern among them, requiring an immense amount of mental energy to do so (twice the effort to disprove BS as to create it, etc). Which is one reason your idea about labeling such beliefs as mental illness would be problematic.
These memes exploit the fact that the human brain is fundamentally a pattern-matching machine, able to discern patterns and connect dots even in randomness. For example, we see animal shapes in the clouds. There's no intelligent designer behind the scenes deterministically drawing animal shapes in the clouds, it's just randomness that eventually creates familiar patterns.
Similarly, with the amount of information the Internet is generating, it's easy to construct pieces of world views that seem plausible but are in actuality constructed from pure randomness. Mix in a few truths to the create an impression that all of it is true. Create enough disparate memes like this that have related threads, and over time entire alternate realities and whole world views can be woven together from them.
Moreover, even the professionals are struggling with this. The entire modern science and practice of statistics, which is fundamentally about distinguishing meaningful information from pseudo-/random data, is still not well understood, or at least not practiced completely reliably. p-hacking, root cause of the Global Financial Crisis, and other examples abound. How can non-professionals who spend most of their waking effort on other endeavors be expected to have a perfect understanding of reality when even the pros don't?
When it comes to memes and mental illness, take the QAnon conspiracy for example. Eg, a cadre of pedofile elites runs the world. Unprovable, but after Jeffrey Epstein and his extensive little black book [1] and suspicious death in custody, plausible. Who's to say whether people who believe things like that are mentally ill or not?
However, regardless of its plausibility, it's not psychologically healthy to allow oneself to get into a habit of believing things like this that you can't know. But, when you're a blue collar victim of the political and financial/business elites deciding back in the 90s to outsource your entire livelihood and way of life to a communist dictatorship, grossly enriching themselves while impoverishing you, any resistance to believing the worst about these people you don't know and can't prove anything about, just vanishes.
Your survival is at stake, your mental energy is being used up on basic survival efforts rather than higher-minded rationality, skepticism and BS-detection. Your mental focus drops back down one energy level from reason to survival, pattern matching takes over, and serves your anger rather than your rationality. When you put lots of people's very survival at stake, that's the unsurprising systematic result.
Map that dynamic to every conspiracy theory on the internet, extend it over two decades of constant trial and error of meme generation and accumulation (most fail, but a few stick and compound over time), amplify it by the apparent premeditated impoverishment of half of US society, and account for the fact that while many memes and conspiracies are plausible but false, some are true, and it's difficult for normal people to discern among them from a removed PoV across the chasm of cyberspace from the actual source.
Are people who believe these things really mentally ill, or are they just the natural state of humanity under these conditions? Maybe it's our higher-minded rational selves that are resistant to the plausible but unprovable that is the unnatural state of humanity.
[1]:https://www.motherjones.com/politics/2020/10/i-called-everyo...