Transgender are freaks of nature. Society rejects them to preserve the continuity of the species, just like humans with apparent deseases. If they are freaks why wouldn't they be somewhat mentaly unstable? Plus the social stigma only worsens the problem.
Homosexualls are almost on the same boat, although they are not freaks, just exibit deviant behaviour. Less social stigma makes them much more social, and society can pretend they are ok.