"Stuck in the wrong body" isn't, how should I put this? The critical argument.
Now I'm not going to answer all those questions directly, as most of them don't apply (I do not believe in a god).
I used to be in the 'wrong body' camp but hormone therapy changed all that along with a whole other mess of psychological problems. It's funny, a shot in the leg makes me feel better than I have in the entirety of the rest of my life. It's quite interesting but I digress, Now I'm not going to speak for all transgender folks as I don't know their individual experiences so I'll just speak for myself and my experiences.
Now I'm not going to lie the science behind all of this is hit or miss. For some it works, for others it doesn't, thankfully we have standards of care for transsexuals. It's called WPATH if you are interested. In there are procedures and guidelines for professionals that know more about this than I do and most of the dipshits on this board. However, some transsexuals can ease their gender dysmorphia via cross-dressing, doing drag, or just simply therapy with a licensed therapist. And good for them, they found something that works for them. However this is not a one-size-fits-all problem. I tried therapy and psychotherapy and all it did accomplish was slap a band-aid on a increasingly festering wound. I ended up on every kind of anti-depressant you could think of, I went through just about every common mental illness you can imagine; anorexia, bulimia, self-mutilation, genital mutilation, suicidal, depression, anxiety, alcoholism, violent depression, obsessive compulsive disorder, and so on. It didn't matter how many shrinks I went to the problem got worse and worse. It just wasn't working. I got to the point where I said fuck it and went to a gender specialist and things started to get better.
I took my first estrogen shot on the 1st of January this year, and literally every single one of those mental illnesses went away in the matter of a month to a month in a half. Transitional Medicine works for me, but that doesn't mean it works for all. Last march I went to another psychiatrist and he had taken me off my a last anti-depressant as there was no need for it (in truth I quit taking it in mid-February). It's proven medicine that works for millions of people who suffer greatly with gender dysmorphia across the planet. A fact so many nay-sayers of transitional medicine like to ignore.
Now there was a doctor who believed gender was a taught behavior, that you could simply 'teach' someone to be a specific gender. In a backhanded way he ended up proving transsexualism. In the case there was a baby boy who through horror of circumcision had his penis irreversibly damaged. So they turned the baby boy into a girl and his parents raised him as a girl, gave him appropriate hormones as he aged, the whole shabang. However something went wrong with all their scheming, He knew innately he was a boy. When the truth was finally told to him he went into a rage. Sadly the rage ended up consuming his life through suicide. A tragedy.
However, in this case it does appear gender is an innate construct within our monkey brains. If this is true universally than transsexualism is a thing.
There are fully functioning women that if you took their DNA and peeked at it you'd be shocked to find 46, XY. That's right genetically male but physically female. It is also possible that a fully functioning male can be born 46, XX that is not a single "Y" chromosome. Now I've established that's possible then essentially concerning gender construct is possible. Is it possible the frame work of female can be born in a male body? Scientifically speaking. . .we don't know. But we do know that a female gender construct and even entire female reproductive system can be made out of XY.
In other words there's a lot of scientific data concerning the issue but we've not figured it out. Which is why Gender Dysmorphia was removed as a mental illness from the DSM.
Is there scientific precedence for it? No? Is there genetic precedence for it? No? Then quit trying to set up slippery slopes.
Gender and gender constructs are not a well understood thing by people who are actually doing the science much less loudmouths on an internet board.
The best answer to the question is "I don't know" rather than 'yes' or 'no'. In the mean time why don't you let science handle what's best in individual cases guided by medical ethics and procedures huh? How about we don't decry medicine that works for millions of people and has probably saved millions of lives. They don't count non-suicide statistics after all.