Who said anything about lying? If Alan Burns says he has a soul do you think that's evidence that he does? People with anorexia starve themselves - by your logic that's evidence that they may be too fat
If they are not lying then it becomes important to find some way of treating them because, either they are delusional or they are in the wrong body.
What would be the best method of treatment? At the moment, the consensus amongst professionals seems to be it is better to let them transition. If some man wants to pretend to be a woman and it makes them happy and it doesn't harm anybody else, why not let them?
People who are anorexic are in danger of doing themselves serious harm, which I would suggest is a very good reason not to indulge them in their delusion of being too fat.
So you are arguing that there is such a thing as a man's brain and a woman's brain - what is your scientific evidence for this?
Many parts of male and female anatomy are different. It sounds plausible that there are differences between male and female brains. I've heard of some studies that seem to support this but they are a little bit sketchy. For now, I'll remain agnostic on the subject.
But you've said that individuals personal experoences that because you don't experience you can't kudge as incorrect. And yet here you precisely do that with reincarnation - your approach is inconsistent.
I dismiss reincarnation because of the science. I don't dismiss people's experiences, only the alleged supernatural causes of them.