Well if you want to talk about my erections, I do prefer having sexual stimulation without them because it brings me closer to the corresponding woman-specific experience. It's a misconception that eliminating testosterone from the body should also eliminate erections, and this can also be understood in terms of female arousal (see diagrams such as this one to note the relatively large amount of female erectile tissue that is internal to the body). Both men and women experience blood rushing to the genitals as part of sexual arousal.

I don't think it has to be shocking that a person with a semi-functional penis is allowed to be in the same room with some partially dressed middle school aged girls. I'm just in there to change my clothes, and I don't take my underwear off (working out in my nice office clothes underwear is an example of the sacrifice I make to minimize my burden on others). I'm not a pedophile, and my sexual orientation is towards men. I've seen women who appear to be butch lesbians hang out in the locker room completely naked for long periods of time, who seem to get a thrill from exposing themselves to younger women (and I've seen those younger women avert their eyes and dress in a hurry). I'm not saying that having lesbians in the women's locker room is a problem, but it's kind of laughable to have this discussion when I regularly see women who are more predatory than I am.

you have plenty of women telling you that we are extremely uncomfortable with your presence in our bathrooms. Instead of empathizing with this and using a more appropriate space, you choose to say what we doesn't know doesn't hurt us. That is not empathy. Far from it.

I've thought about that as we are having this conversation. But I think "what you don't know doesn't hurt you" is a fine application of empathy, because I am taking care to hide facts (e.g. my penis) that might hurt the women in the restroom. I'm sympathizing with the potential discomfort they would feel, and I am taking care to avoid that discomfort. It's like tip toeing quietly next to a person who is sleeping; taking care to hide my presence to avoid disturbing and bothering someone else. It seems pretty empathetic to me, considering that I'm going far beyond what the law requires me to do.