The obstetrician judges solely on reproductive organs, likewise the botantist (there are edge cases for both, which you gloss over) not so for people in the street, and neither can you reasonably say that they're inferring about genitals, they're inferring about gender/sex and thinking about genitals from there if at all. Fertility is a proxy, but not what the arbitrary distinction actually is, even if the arbitrary distinctions and assumptions themselves inform evolutionary processes that are fundamentally concerned about fertility. By that measure, all one needs to transition is hip pads and greasy hair. But those aren't the only factors being looked at, because social pressures and evolutionary ones have built up all sorts of standards perhaps best described as gender (in the linguistic sense of attributes/classes of nouns; since certainly other measures of fitness than simply fertility are evaluated) rather than sex per se.
My usual approach here is to consider whether information is hidden. If there is nothing you can reveal to dissuade a consensus that you are male, then you are male. If there's a consensus that can be dissuaded, then I suppose you have a secret identity.
How do people typically judge gender? In the case of both the obstetrician and the average person, they do so with reference to fertility, something like "resembles sometime female-fertile". For both observers, sometimes they will have no clear judgement. And they both make do with the evidence they have.
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How do people typically judge gender? In the case of both the obstetrician and the average person, they do so with reference to fertility, something like "resembles sometime female-fertile". For both observers, sometimes they will have no clear judgement. And they both make do with the evidence they have.