I haven't got to the end of the thread, but I'd like to thank RatRolyPoly for giving it a go.
Room full of people, I pick out all the women. Truth is I don't know what's in their pants or what chromosomes they have, you might say I do because someone's dog always barks at their brothers or some such, but the bare truth is that I don't.
Same room of people, I ask people to tell me whether or not they're a woman. Those declaring themselves women may or may not be the same people I thought were women, and whilst they certainly know better than I do what's in their pants, we're not going to be asking them to prove it any time soon.
I once said on here (got quoted on the BBC too, preens) that I'm fully in favour of transwomen being treated without discrimination and in a dignified way in the 99% of cases where biological sex doesn't matter - it's the 1% where it does that I'm worried about.
And in a sense, that 1% boils down to the small number of situations where it becomes apparent or matters what is in the person's pants (or where, given what we know about how people view their own bodily autonomy, it ought to be apparent to the trans person that even if they pass this is one of those situations where it matters to the other person).
So - communal changing rooms where people get naked.
Overnight accommodation, whether shared voluntarily (e.g. sleeper berths), compulsorily (closed psych wards, prisons), or somewhere in between (e.g. homeless shelters, where women aren't compelled to stay, but don't exactly have a choice about alternative accommodation).
Medical examinations of genitals/breasts, where, if you have an ounce of empathy and compassion (surely a pre-requisite in an HCP), you'd realise that a woman would feel very differently about the situation if she realised you had a penis under your surgical scrubs (and in fairness, she may well realise, because you may well not pass as well as you think you do).
(There is also the further issue of discrimination, and affirmative action to overcome discrimination, and whether one thinks that discrimination has its roots in recognising people as biologically female, or as conforming to gender stereotypes. Or, TL:DR Pippa Bunce. But that's probably for another post once I've read the rest of the thread.)