If one is suffering from an intractable lifelong mental illness, and it comes down to suicide being their only option in finding release or relief, will they be punished in the hereafter for taking their own life?
An anhilationist Christian such as myself would say 'No.' A universalist would also say 'No'. So would a Quaker. Catholics -- not sure what they'd say. Some would say yes, some no.
Protestants would I think come from this position: If you believe that God punishes people forever in the afterlife, then yes; however there are caveats since the reason you kill yourself matters. It could be considered an accident or due to your mental illness. That is certainly what is the common answer from many groups which believe in eternal flames of torment. Yes, from what I have been taught. On the other hand many people in these groups will disagree about it. You won't find a unanimous point of view even among them.
It complicated by the fact that it is a mental illness. A mental illness causes people to do things that normally they would not, so the question has caveats. You could probably go to any church, not believe that suicide was an automatic hell ticket and still be accepted. You'd find disagreement from some, but it would not keep you out of membership in most churches.