For me I'd like to see a post gender world where sex didn't matter for most things. That would mean that in the case of your colleague it wouldn't matter what you "saw" her as because when you're working with somebody their sex is totally irrelevant to you. You are not performing medicine on them, you are not having sex with them, you are just working with them. Why should it matter whether she is male or female any more than it should matter if she is blonde or brown haired, if her blood group is A or O? There are not very many jobs where a person's sex and by extension gender matters. But we are not very far forward from a time when it did, when men and women were considered so different that we did different jobs and had totally different strengths and roles.
When you strip everything else down, there are two situations where sex matters and that's biological reality: things like the shape of someone's body being different, the ability to get or make somebody pregnant - infertility issues aside - the possibility of menstruation, the ability to pee standing up. These are things which need to be accounted for; women need facilities to deal with their periods in public, private and workplaces, we need to know somebody's sex if we plan to have children with them, pregnancy is a characteristic which needs protection e.g. for health and employment purposes, we have different requirements in terms of safety equipment, medicines and the shape of form-fitting clothing.
The other situation where sex matters is in the context of sex based violence. That is, the ability to rape and the possibility of being raped. Domestic violence likelihood, effect and outcome differs by sex of perpetrator and victim. Honour crimes. Many, many different possibilities all under the heading of male violence against women. This is such a serious risk that even people who claim sexism is dead understand the need for refuges, rape crisis centres, single sex prisons and hospital wards, laws against date-rape drugs, and the age old advice for women not to do anything which puts them at risk. They might argue that these services are equally needed for both sexes (they aren't, the statistics show us this) but they will not argue that they aren't needed. We may argue against advice which puts the onus onto victims to prevent attacks, rightly IMO, but that doesn't change the fact that most people recognise there is enough of a trend for that advice to exist.
Transactivists are usually on board with the first reason, even if they prefer to use gender-neutral terms to describe these needs. The second is more problematic and usually ends up with lots of shouting about who has it worst, which doesn't answer the question of whether these facilities are needed and why if they are needed transgender people need to swap to the other facility. Any suggestion of having totally separate facilities is then met by cries of discrimination, as though a women's refuge or prison is some kind of club that you can't get access to, not a place that nobody wants to end up in in the first place.