That's not persecution and it's certainly not "opposition to their right to exist", which was the original bullshit claim. Anyway, the APA (a very left leaning organization) diagnosis for transsexuality is Gender Identity Disorder (GID).
Your information is out of date. Being transgender itself is no longer considered a mental disorder. Gender dysphoria, discomfort and dysfunction caused by society and by being in the wrong body is the diagnosable condition. Once transgender people have been treated, there isn't any more dysphoria and there is no disorder.