Due diligence. There is the temptation for some to get on the gender band wagon. However the two things to look out for are consistence and Insistence.. If the child just say, I am the wrong gender, then you want to make sure that it is not a flash in the pan. If they say it once or twice, fine. But if they keep saying it and are very insistent about their gender, then as a parent you need to listen.
Stonewall have done a lot of research with regard to under 16s. 45% of trans school children have attempted suicide. 85% self harm. This is true until they come out and get support. So this is not about some moral perversion. This is about doing what is right for your child and if that involves them living as a different gender, as long as they are healthy and happy, then that is what you do. Or would moral outrage give you licence to see your child die?
I know which I would choose. This is about putting away foolish arguments, getting your adult pants on and being a responsible parent.