Well, here is my opinion on things, as a gg.
If someone walks into the bathroom who looks like, or is presenting as female, I'm perfectly comfortable. It's not the genitals that bother me really, it's the presentation. As long as you're somewhere on some kind of female spectrum, I'm not uncomfortable.
However, one time I was using a gender neutral bathroom with stalls, and a man walked in and used the stall next to me. [I knew it was a man because I heard him speaking as he walked in, and then I saw his sneakers and the bottom of his pants and he peed standing up.] I felt very uncomfortable. And I actually thought about why I felt so uncomfortable, as I was sitting there [I waited for him to leave because it would have been really awkward to wash my hands next to him. I didn't know if he even knew I was there.]. It wasn't something I would have expected to bother me so much.
I came to the conclusion that it was the fact that I was not used to being in that situation and it made me feel, instinctively, a little unsafe. Women are very vulnerable in public bathrooms. "Don't go to the bathroom by yourself because a creepster might hit you over the head and rape you or peek under the door at you." It's pounded into our heads so we can be a little paranoid. But I didn't get upset because it
was a gender neutral bathroom. I had to suck it up, there was nothing I had the right to even complain about.
Anyway, I feel like women, any women, have the simple right to use the bathroom. When it comes to safety, I think whoever is in the most danger has the most rights- as in, real danger trumps mere personal discomfort. In most situations, a transwoman would be in the real danger- if she was forced to use the men's bathroom, all hell would break loose. It wouldn't be 'discomfort,' it would be the risk of bodily harm and the ruin of a reputation. On the other hand, any discomfort a gg might feel at having a transwoman use their bathroom would only be perceived danger, not real danger. So the gg would have to suck it up. I would tell her, "this person is a woman, therefore she will use the woman's bathroom. If you don't like it, it's your choice to find a different bathroom to use, but not your right to kick her out."
Those are my thoughts on the matter.