The reason gender dysphoria isn't classed as a mental illness is because it describes the distress a person experiences due to the underlying condition which is often a biological birth defect. Read how the APA classes such things for a clearer understanding. Of course such a condition can take it's toll on a person's mental health which is evident in the suicide rates that detractors of LGBT support seem to relish reminding us of, despite the fact it is also evident that appropriate treatment, that includes transitional surgery, has significantly lowered that rate among transgender people. But you're right, there are too many insensitive types that when they talk about mental illness, and not just in relation to transgender identity, they are only doing so in an effort to stigmatize the issue. Case in point, you have someone like "Stefoknee Wolscht" who says "these people are sick" but not in such a way that he actually cares about their well being, he quite clearly doesn't give a s**t about them and is more concerned with where the next freak show is so he and his cronies can go chase them with their proverbial pitch forks.