"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 classify it as M or F, and most people will agree for any given person whether they are M or F. It's quite easy to see why that's what matters: if you get a public safety alert on your phone about, say, an "asian male, middle-aged last seen at ..." do you think, in the rare cases where they differ, that this refers to reproductive role or appearance? Let's hope it's appearance!

In daily life, outside of dating perhaps, most people generally don't care about someone's reproductive role. In a public bathroom, most don't really care what's actually between someone's legs so long as the individual looks like they belong. The authorities almost always care about sex only as a visible characteristic for distinguishing people. When you say the common meaning refers to reproductive role, you are probably saying that only because it's a proxy for the aspects of one's sex we actually care about.

This recent obsession that when we talk about someone's sex we obviously mean in a reproductive capacity regardless of context is a totally political fabrication in my opinion, and there's no good reason for a passport agency to prefer that definition. I believe the information on a passport is meant to help identify an individual -- so common-sense sex, i.e. appearance, is most important. (Similarly, requiring trans people to use the public bathroom they don't visually look like they belong in is only going to cause chaos, if they obey such a law.)

[1] https://www.lesswrong.com/posts/4FcxgdvdQP45D6Skg/disguised-...