I'd like to draw everyone's attention to the link in the image. Specifically the title: "High Suicide Risk, Prejudice Plague . . ." Prejudice. That's the key word. It's almost as if the very article they cite is saying that the cause of the high suicide rate is external. It's caused by societal rejection and not the gender dysphoria. Ergo, being more accepting of transgender individuals, such as by allowing them to serve in the military, may reduce the suicide rate.

Jews stuck together. They would try to stay alive for the sake of their families. Trans people have frequently been rejected by their families. They feel more despair than fear; the survival instinct does not kick in a strongly. There may be other factors as well.
Maybe prejudice is the main factor and maybe it isn't. But in case it is, it shouldn't be used as a basis for further prejudice. If discrimination plays a role in elevated suicide risk, then using elevated suicide risk as a reason for discrimination would just cause a cycle. In any case, there are other reasons to reduce prejudice.