“Male”/“Female” is on the sex side, based purely on things like reproductive organs, chromosomes and hormones.

Not really, I don't think. They're just the adjectives where woman/man are the nouns. If you talk about a male coworker I assume he's a man, not that you checked his birth certificate.

Male and Female are still normative exclusionary categories that describe trends within physiology and not hard rules or limits. Sex is not a golden rule. It is a human created category in the same way gender is.

If you want to talk about specific anatomy there is no reason why you can't talk about the anatomy you're referring to.

I would also point out that referring to trans women as male woman is very derogatory and is functionally the same as calling us heshes or shemales.

Sex is a lot more complicated than male/female. There's a bunch of different sex characteristics that make up "sex" and people can have all sorts of different combinations of them. If you just use a male/female binary, that doesn't tell people what sex characteristic you're referring to. Maybe something affects people based on chromosones, in which case people who are xy but otherwise "female" (like with cais) would go in the "male" category and vice versa. Or maybe something affects people based on hormones, in which case transgender people taking hrt would have to be categorized based on that. If you say "male/female", no one knows if you're talking about hormones, or genitals, or chromosones, or gonads, or whatever else, so it's best to be specific and use language like "people with [body part]"