Haven't RTFT but to address the OP regarding physiology being proof that trans is not mental illness.
My husband has major depressive disorder, also known as clinical depression. Amongst other things factoring into his mental health issues are hormones, neurotransmitters and brain wiring. Certainly there's a strong genetic factor in play given his family history. He will likely need to be on corrective medication his whole life - luckily he responds well to this.
Depression is categorised as a mental illness but it is also - in many cases - a physical one. Certainly it has physical effects in all those afflicted. MRIs show vastly different brain activity to the normal function as well as a smaller hippocampus and other structural differences, including fewer seratonin and opioid receptors. Adult depression has been linked to Alzheimers and is likened to a form of brain injury or a dying of the brain in certain areas.
I haven't researched other conditions but I'm betting all mental health conditions have some form of physiological causes or effects. They're categorised as mental health because they have to do with mood, thinking and behaviour - not because they are somehow intrinsically less-than other medical diagnoses (though that absolutely is the history and the stigma).
We do a disservice if we resort to one mode of diagnosis and treatment for any condition without asking why that person is feeling the way they do. We also do a disservice when we equate feelings with facts and that they alone decide the outcome - my husband would be dead if that were the case. And again, we do a disservice to think that physiology rules out any kind of mental health issue - because that is patently untrue.
And please stop talking about mental illness like it is something icky you stepped in. If trans was indeed a mental illness it would be no less deserving of understanding, support, compassion and treatment than any other explanation of trans would be. The fact people fight so hard to be NOT under the umbrella of mental health speaks volumes about how much contempt our society still views those illnesses with.