I am supportive of people's right to live with dignity and respect, and I agree that asking in front of a waiting room is undesirable (I have had that same thought in other waiting rooms, too), but I feel like a medical analysis setting is one in which biology (sex) actually does take precedence over identity (gender), because that has implications what and how things are analyzed.
That said, transgender persons taking hormones will have much greater variance in ranges of everything. I think it's sensible to have additional gender markers in addition to sex.