No one has said that it wasn't a mentally based issue.
But you do raise a valid "point". Since it is mental issue as suggested, then which is the right 'answer' to achieve the safety and health of the patient, the parts of the body are the "correct" identifiers and should be adhered to or the mental knowledge that you are ___ Gender?
I believe that the people who are 'confused' about their gender have altered mental pathways. To correct this, there are 2 options: 1. fix the pathways. 2. Fix the body to match the pathways. There is no known method right now to do #1 without any harm to the patient so #2 is the only option to 'balance' the mental pathway and perceived gender.
Given this, I take the approach that since their choice has no bearing on my life, I don't care. If I use the wrong pronoun, I will correct the pronoun next time I address them. Since most bathrooms have stalls, there is no issue there. I have yet to see how their choice can affect me in any way.
I do think it is unfair to allow genetically born males to compete in female sports. But if we are going to allow that, we should just get rid of the male and female split and have one set of sports. That will solve that problem. They could also solve the problem by putting hormone replacements on the banned substances list for competitions.
That is my opinion and I am quite happy with it.