"Mental illness" is a very broad term, and depending on who you ask, it will include certain typologies or not. I personally wouldn't consider mental illness anything that doesn't have a serious negative impact on the person in their life, or the life of those around.
With this being said: yes, I agree that psychedelics have a high potential to unleash mental problems in people. They are not only amplifiers, they are destabilizing by nature, in the sense of disrupting the usual mental patterns. This can be very useful and can even become part of a new type of balance, but it can also leave someone who was already on edge in a very bad state.
I have personal experience with this. I first had psychedelics when I was 18. It was a moment of change in my life, as that age usually is. I had been living for many years in a bad situation with a lot of suffering, but was very unaware of it. And I was severely underdeveloped, emotionally. My first trip was with mushrooms that I grew, a low dose. I remember some Escher-type visuals, but most of all a feeling that something was terribly wrong with me and maybe reality itself. Like a stain on my soul.
My mind was already on edge, and psychedelics tipped it over the line. I fell in a severe depression with bouts of compulsion, strong anxiety, self-harming behaviors. I didn't understand what was going on and thought that it would improve by going deeper on the roots of the issues, so I tried to go deeper with psychedelics. It was all too much at once, and it only made things worse. Then the problem got even worse when I was overmedicated by a so-called psychiatrist, but that's a different story.
I got many good and helpful lessons from psychedelics even during those years, but it was not the right moment for me, and their overall effect was more harmful that good. at least the short and mid term effects; on a longer timeframe it's hard to say. But after my first experiences I should have stayed clear from them until I was more stable, I eventually did that.
What I learned from this situation is that one needs a minimum of stability for doing that kind of work. Psychedelics can help tear down outdated, maladaptive, or otherwise not very good mental structures, but there also needs to be some time to build something different in its place.
I don't know if it's a similar case for people who go into psychosis, maybe the causes there are different, although (besides a genetic predisposition) there often seems to be an aspect of overdoing it and not leaving time for integration. Probably someone else can offer more insight in how psychedelic-facilitated psychotic delusions feel from the inside. With pharmahuasca in particular, I've often had some "insights" about myself or reality that, while true in some kind of metaphorical way, would be very problematic if literally believed. So I wonder if there could be some factors related to this that could contribute to this kind of psychosis in some cases. To be clear, I'm not saying that all or even most cases of psychosis are caused by this. But I could see how someone who has never thought about any kind of metaphysical or spiritual topics and suddenly has an extreme experience that points to them apparently having some privileged, "special" knowledge about the nature of reality could more easily end up believing it.
Probably it depends on cases. If they are more open to conversation, listening to them and offering some understanding of their experiences without either judging them or supporting their delusions could be helpful. If it's one of those cases of strong messianic delusions where they have the ultimate truth and you're just an ignorant idiot jealous of them, I don't see a way to have any positive effects, and many ways to have negative ones.
