I think it is ridiculous to say that "male" and "female" are just labels.
The entire natural world is divided into male and female, there are clear characteristics that distinguish the male from the female humans and any other species.
If a human skeleton is exhumed after 1000s of years, it can be determined whether it was a male or female.
To acknowledge a difference does not imply the acceptance of any theory saying one is better than the other, which is a ridiculous argument in itself. Male and Female are obviously equally important/valid/necessary.
To say that there is no significant biological difference, and it is all just labels put on people by a bigoted society is disingenuous or even naive.
It is like saying we all have the same skin colour. No we don't. However, obviously, skin colour is not important, and one colour is not superior to another. We do not need to say that no difference in skin colour exists to come to this conclusion.
To me it feels wrong to have to call a man with his penis taken off a "female", as to me, being a female does not equal man minus penis.
Maybe transgender patients should be seen as a "third sex" ? Or just be officially the sex they ARE (and which is unchangeable) but be allowed to call themselves Ms. in their lives.
If a friend would prefer me to call him "her" from now on, with or without operation, I would oblige. And I have no trouble with transsexuals using women's toilets, (but I would have no trouble with men using women's toilets either. I don't really see why men's and women's toilets should be separated anyway, after all, you lock yourself into an individual cubicle for the bit where you pull your pants down anyway.)