She is a trans woman. She is a woman. Within the context of medical access, from what I can gather she has a penis, she has testes, and she doesn't take hormones currently (she might but a comment she made suggests she doesn't). That gender-non-conformance doesn't make her any less of a woman.
I'm not sure what your hangup is with respect to her? She very clearly present herself as a woman. And women with beards, sharper facial features, or deep voices aren't terribly uncommon nor do those aspects make them any less of a woman. Women like Harnaam Kaur exist and they are just as woman as any other woman.
https://www.youtube.com/watch?v=HB85apiZgFg
> Should he be allowed to whip his dick out in women's bathrooms?
Should she.
Should she be allowed to use a woman's bathroom as intended? Yes. No questions asked.
Now if someone was doing something problematic in the bathroom (flashing/exposing genitalia or breasts) and/or harassing other women in the women's bathroom then they'd need to be removed. Not because of their gender or because of their features but for the behavior. It's a very simple and straightforward concept.
> If actual women complained about his presence in, say, a support group for mothers, what would you say to them?
Her presence.
If she is a mother she should be permitted. If she isn't a mother/doesn't have children then there is an argument to be made for denying her presence there. If she has children but it was a support group exclusive to birthing parents then again there may be an argument. But more often than not those support groups aren't exclusive to birthing parents and they aren't even exclusive to women.
> Should he be allowed to join a women's boxing club and punch women in the face?
Should she.
And the answer is that it depends.
If it's at a competitive or professional level then she is subject to the rules of the club and if they require certain hormone levels to participate then that's the nature of the beast. I personally don't see it as necessary but if it's the requirements for participation then that's what they are and the best you can do is fight to change them.
Now if the club is a hobbyist or non-varsity/school club then absolutely they should be permitted to participate.
Either way whether they are technically permitted, I think they should be allowed to participate regardless of testosterone levels or anything else. Boxing is divided into weight class anyways so there's little flexibility for testosterone influencing being "bigger".
> And so on. I'm sure you get the idea.
I understand what you are saying but I just outright disagree. Trans women are women. Intersex women are women. Non-gender-conforming women (regardless of whether they are cis or not) are women.