Earlier quoted context omitted.
"Sex" is a disguised query [1]. I would not agree with you that the plain and common meaning of sex is that it's the reproductive role (which for many trans people is "permanently sterile" anyway). If you run a clothing store, you don't care about reproductive role, you care about whether someone wears men's or women's fashion. In daily life, a stranger's sex is entirely their appearance: we make a snap judgment to c…
I mention reproductive role (gametes etc.) because that’s what sex is, not because it’s the sole feature of interest. Why we care about someone’s sex is a different matter. Sometimes we don’t! You can sell someone a coffee, and their sex has little bearing on the situation. But sometimes we do care about their sex, because their sex has material consequences. Perhaps sports are the most relevant example to this discu…
There are many definitions of sex. Some would say that sex should be defined chromosomally. I think it would be very unhelpful to put an M on a passport for an XY cis woman -- it should be an F, or maybe an X, if X were just a marker to indicate an unusual edge case. If so, shouldn't transgender people at least be afforded an X on their passport?
And then there's what's between your legs. Well, this is surgically alterable to some extent, so do you mean what's currently between your legs, what appears to be your legs, what was between your legs at birth, etc.? Or do you mean reproductive function? Maybe someone might say that a regular surgery isn't sufficient to change sex, but stem-cell-grown genitals do count as changing sex.
Regarding outward appearance (etc.) being correlated with "sex" (however it's been defined) -- that's exactly my point! In fact, because outward appearance is what is important nearly always -- except possibly in dating, reproduction, and sports -- and because there are a plethora of different meanings when sex is defined as "biological truth," I honestly think that outward appearance (etc.) is what most people actually mean when they say someone is a "man" or a "woman." Therefore, sex, in common usage, is appearance (etc.). This matches with how a tomato is a vegetable culinarily (i.e. colloquially), but a fruit botanically (i.e. "biological truth").
(Anyway, all this is really beside the point of this thread. You can disagree with everything I've said -- I'm just trying to argue that the U.S. is presently a difficult destination for transgender travellers.)