In the end though - why does it and should it matter? Why do people have a problem seeing those who exist outside the XX and XY binary as being people?
There is not a problem seeing these people as people. Lots of people are mentally ill, but most don't expect the rest of the world to deny reality to participate in their mental illness. Allowing biological boys/men compete in sports as girls/women is not fair to biological females. Its wrong to allow a boy suddenly declare himself to be a girl so that he can use the girl's restrooms and locker room. It's wrong to allow children to make the decision to take hormone blockers or have transgender surgery.
When something appears to be hardwired in a person is really reducable to just a mental illness? I think each issue needs to be treated seperately.
When it comes to using what restroom, I doubt a boy can simply claim one day, to be trans, so as to use the girls locker. Doesn't there need to be a bit more documented history first?
I do appreciate the concerns, they are valid in some ways but not so much in (for example the impression I get from some that trans people are just perverts waiting to molest someone).
In athletics though, I 100% agree it would make a mockery of women's sports, because biological identity is what creates the need for seperate leagues.