I would have been okay with a less toxic choice (replacing "women's health" with "gynecological health," for instance), providing the trans lobby paid for such a neutral change

I doubt TRAs would agree to that given that you'd just be saying the same thing but in Greek rather than English ("gyne" just means woman).

Weirdly, no one seems to be campaigning against changing the name of the gynecology specialty, or choosing some other word for birth attendants rather than "midwife," and every single advocacy organization with "women" in its name that is lecturing us about "inclusive language" is not making one move toward changing its name.

And it's a shame, it'd be really funny if NOW changed their name to National Organization for People because the acronym would be NOPE which is my answer next time they ask for donations.

[–] Lipsy #bornnotworn 0 points

NOW won't stop being NOW. Organizational names rarely, if ever, change.

Witness the NAACP, still so called even though "colored" has been considered a slur at least since the '60's.
The Mississippi University for Women has been co-ed since 1982 (a condition of either Federal or public land-grant funding, I think) but still has that name, nicknamed "The W".