I feel two ways about this topic. First of all, I completely agree that for many people, the views of society may be a massive player in whether they are suicidal or not, and it is despicable that we are allowing and overlooking the hatred and misinformation feeding negative views of transgender people. I seriously believe that we need more awareness and education to help move things in the right direction. It won't be easy and it will take a very long time. Social stigma is still directed at homosexuals, but their civil rights have come a very long way, and the rights of transgendered people can as well. It won't solve everything, but it will help.
There is a different side to the story though, but one which would be extremely hard to do any research on, as it involves those who do not accept themselves as transgender and possibly do not even accept themselves as different. Much self-harm and negative thoughts may be related to not yet seeing or accepting one's gender identity.
For example I have accepted myself as a transgender person, and accepted the fact that I am male and that being born female was a problem but one that I am overcoming. Now that I have accepted that, I really don't feel the sadness or hurt or anger that I did before. It outrages me when cisgender people spew anti-trans nonsense and the discrimination bothers me, but as a whole I have become a content and happy person.
Before I was trans, it wasn't impacting me directly what others thought of transgender people. That wasn't on my mind. As a teenager, plenty of other negative things were, though.
I used to under-eat. I was never anorexic, but I would be considered normal in comparison to many of the Eastern European and Russian women, which are usually very very skinny and many American women would label them as much too thin. I liked not having curves, being able to see my ribs and collar bone ever so slightly. My doctor didn't mind me at that weight, but he did not want me to get skinnier. I now realize that is because I was disturbed by and would not accept a female body shape. Androgynous and very thin was not as good as masculine to me, but it was better than looking feminine to me. At the time, I didn't understand why, I just understood that I liked being skinny.
I also got interested in animals a lot. I liked to draw myself as an animal and make up characters. I would even immerse myself in books and video games basically every free moment, rather than interacting a lot with people. The only 'real' thing I liked to do (virtual reality and books being theater of the mind) would be spending time with my pets and concentrating on them. This lead to me spoiling my pets and taking extra good care of them, but it also meant that I was spending time in worlds that weren't real with the books and games, because I didn't want to be present for my life. I didn't realize that 'living like a female' was the problem, I just knew that I preferred the escape.
Unfortunately, there were also times when I would be overcome with sadness. My emotions were haywire and I was under constant stress. Constant and intense. I would get mad easily, sad easily, fall into depression sometimes. Yet I couldn't identify the underlying problem, and yes there were times as a very young person when I felt that I would rather be reincarnated than live the life that I was in, but I couldn't bear the thought of leaving my pets and I couldn't be sure reincarnation was real.
Since coming out as trans and living the life I have always wanted and tried to artificially live in books and games, I have lost all of that hopelessness and craziness. I feel much better, happier, complete. I believe many other struggling teenagers may actually have 'cryptic' clues toward being transgender, yet they themselves may not even understand what is causing their feelings. I hope that someday there will be more ways to help them.