Trying to arrive at a definition by identifying essential traits is linguistically misguided. "Woman", like many words (including "chair" and "horse"), has an ostensive definition -- it means "one of those". A language learner learns what that sort of word means not by being taught criteria but by observing which things other people use it to refer to. Which things are in the "those" set is determined by the collective perceptions of the language community.
This is in some schools called a "cluster concept": a concept from a cluster of ideas or examples as center point for an idea
In those same schools, one of which I happened to go to some years ago, we learned right along with the idea of "cluster concepts" what such a cluster concept definition could be used to leverage.
Inappropriate uses of cluster concepts yield themselves to the "no true Scotsman" fallacy.
It is something that genital format exclusionists, (transphobes) fall into. It's one you are falling into, because
one cannot say there is any "true" satisfaction of a cluster concept.
Cluster concepts, at times CAN imply the existence of an adjacent real idea or a set of ideas which interact together, a much more complicated relationship existing beneath the surface, but the cluster concept must be abandoned for that to happen. It can only be "generally" true, but that isn't actually being correct. It's quite literally being wrong.
Now, the cluster concept of traditional "man" and "woman" is giving way to more complex understandings, understandings which recognize it's just not important to have a genital configuration, when discussing whether someone is "one of those".
What matters for this sake is that you don't get to decide for someone else which of these they are. We as a society are coming to recognize that's something they decide.
You shouldn't make snap judgements about who someone is or what someone wants or whether they want it from you by the shape of their body or the clothes they put on it.
How's this for a cluster concept: it's in the neighborhood of "you still have to ask".
You can choose not to respect that, to some extent, but the respect you receive will come in kind.
You have a mouth, it makes words come out of it, just... Ask. Ask what people want. Then, if it's something that you do for other people who you don't even trust, you do it for them, too.