Ogling? Do you think I would ogle? I assure you I am perfectly capable of being in the presence of naked women without ogling. It was something I was capable of as a young man, and it has grown much, much, easier as I have grown older.
I don't think my behavior inside the locker room would be an issue. I think the offensive behavior in question would be walking through the door. It isn't my behavior that is offensive. It is my presence. It makes the ladies feel uncomfortable. As a kindness, I will not attempt to go into that room. Just in case my kindness is not enough, the management of the facility or possibly the police will assure compliance.
On the other hand, if I use the room for its intended purpose, I would still have to expose myself to them, and that, too, would cause discomfort, although the reasons for that discomfort are often misunderstood. Seeing a naked man is not something that makes women, or even girls, recoil in horror. It is just that if they, themselves, are likewise fully or partially disrobed, the presence of the man makes them nervous. If they see physical evidence that I am indeed a man, then they will not only be in the presence of a man while they are undressed, but they will be in the presence of a man who is not conforming to social conventions. If I am kind, I will not create that anxiety in them.
This comes up very often in debates around high school locker room access. Even if the girls do not see the person's penis, they will have grown up with that person. They will know that person does in fact have a penis. Fortunately, in every single case I have read about, there is a perfect solution. Since there is only one transgirl, there is a very convenient separate facility where a single girl can change clothes by herself. Using that would be kindness, on everyone's part, and yet that solution is rejected.
I can't see why it would be. It seems that to do so would be to be treating the other girls kindly, and yet, it is rejected.