I think that the link between philosophical positions and mental illness probably goes beyond the scope of the dangers of specific red zones of philosophy. Having worked in mental health care, I have seen that people's belief systems come into play in connection with mental health problems, but it involves many factors.
I am also a bit wary of discussion about mental illness on this site, because I am sure that it is probably experienced by certain members of the forum. I have also noticed that in a number of posts in recent weeks that people have made comments, telling people that they were mentally ill purely on the basis of something that they had written. I made no comment because it was in the context of specific interactions, but I was thinking that people should not be throwing labels around in such a way. Mental health problems involve careful diagnosis and, even though the antipsychiatry movement is out of date, I believe that the way people are diagnosed is an area which involves critical interpretation.
Leaving that aside, I think that the relationship between mental health and philosophy involves the link between how our ideas affect our intimately. I am sure that there is research on the topic but, based on my experience of working in mental health, part of the problem of that, as people, we view ourselves in frameworks of ideas connected to our experiences. In times of heightened stress, these ideas may become exacerbated in the struggle to make sense of life. Also, the quest for finding ideas which make sense can involve a lot of stress.
However, based on my observations, I have seen people getting unwell, and I am speaking of their experience not diagnosis, when their ideas become incredibly overwhelming, especially if they lack other people to discuss the worries which they have. But, I have known people experience this on account of their engagement with religious philosophies or other ones, including but not specifically nihilism.
I also would say that mental health problems is likely involve many factors, including genetics, but it does seem that philosophy comes into the picture in the way people interpret their own mental states. But, this is such a big area beyond the scope of this thread, especially in considering the way people interpret aspects of psychotic experiences.