The Attorney General, as the first law officer for the Crown, will appoint the person.
I don't know who would be involved in the decision, but senior politicians in the government of the day are probably involved.
How many commissioners have there been, to date?
Six.
https://en.wikipedia.org/wiki/Sex_Discrimination_Commissioner
Do you think that a straight woman would likely the best candidate to head up a commission on gay men's health initiative?
Why do you keep asking these questions, knowing what my answer is going to be?
A straight woman may very well be the best candidate to head up a commission on gay men's health. For such a post, I would expect a medical expert in sexual or public health to be appointed with research or clinical experience in gay men's health. Would there be any women in such a position?
Do
you think every single medical expert in sexual/public health specialising in gay men's health is a gay man, and therefore excluding women from the role makes no difference?
The gender and sexual orientation of the person are irrelevant and it is morally undesirable to claim that they're relevant when they are not, and discriminate against people on these factors.
And once again, you've made a misleading analogy. A gay men's health initiative is presumably specifically set up in the interest of improving gay men's health. It's excluding all genders and sexual orientations excepted the named ones.
The role of Sex Discrimination Commissioner is set up to oversee and uphold the Sex Discrimination Act, which protects all genders and sexual orientations from discrimination in employment.
You
could mount some argument that a gay men's health initiative is best headed by a person that 'resembles' the targets of the initiative (although as I've said,
I do not accept such an argument); but
how much the less could you possibly say that women represent all genders and sexual orientations in terms of a Sex Discrimination Commissioner? By definition, any single person could not.
By the way, I have so far not questioned your assumption that people 'on the inside' have a valuable perspective not attainable to those on the outside. Yet you discount the perspective of someone 'on the outside', as if an outside perspective could not be valuable, or in fact,
more valuable. If, for example, discrimination against women in employment comes from, in part, a work culture attuned to male interests, who is going to have the insider perspective on these interests -- a man or a woman? Women do not know what goes on behind closed doors when only men are in the room; they're incapable of leveraging off information they do not have as outsiders.