- all transgender people can cross over into gendered spaces, regardless of what their genitals, mammary glands and body hair might look like; BUT the onus is then on them to ensure that they either eliminate or minimise showing any parts of their bodies which might reasonably offend others of the same gender within that space;
Sounds reasonable, at least until you think about it for a bit. So, let's think about it.
I don't know whether it was your intention, but the above sounds like the offensive aspect of sharing a locker room is that they might show their body parts, or that the showing of body parts might reasonably offend someone.
Perhaps that was just poor phrasing on your part, or perhaps you have fallen into the failure of comprehension that befalls people again and again and again on this topic. The problem is not your body parts. The problem is my body parts, with "my" being the person who is undressing, especially a woman, including a teenaged girl in that category. She is concerned that her body parts might be seen by someone she does not want to be seen by.
Remember the phrase, "Can she put the towel over her eyes?"
So, keeping the "offensive" body parts concealed is a necessary, but not sufficient, condition for solving the problem. It is necessary, because as soon as the "offensive" body parts are seen, the woman who sees those parts will know that the person is male. If the body parts are concealed, it is conceivable that she won't know, and what she doesn't know won't hurt her.
However, it is not sufficient, because there may be some other way for the women to know that the transwoman in their midst is a male. This is especially important in school settings. In a high school, everyone knows that the person is male, so it wouldn't matter if the transgirl never removed a single stitch of clothing, the girls would object to her presence, because "she" is a male, and the girls do not want to take off their clothes in the presence of a male.
There is no solution to the problem that also allows the transgirl and the girls to use the same locker room. Either you have to tell the transgirl that no matter what would make her feel good, the girls do not want any male, including her, to see them undressed, so the transgirl will have to use a separate, private, facility, or you have to tell the girls that their desire to not be seen naked by someone with a penis is unworthy of consideration and their request will not be honored.