(1) They're not XX parts. People with XY chromosomes can have them,
either because they're trans or because they're intersex, and those
people also need & can have trouble accessing related medical care.

I think the way you phrased this is kinda confusing. If someone has a vagina and also XY sex chromosomes, it won't be because they're trans; from what I understand intersex is the only thing we currently know of that can cause that genital-chromsome combination. They might happen to also be trans on top of being intersex, but trans identity in and of itself is not the actual driver behind being a vagina-having, XY-chromosome-possessing person.

Totally agreed on the second point though, calling a service whose users include trans men a "women's" anything feels invalidating and misses the point.