I understand the distinction CIG is making, I just don't think it's a legitimate concern. If sexual assault is the issue here, then focusing solely on trans-people is a red herring. If being comfortable in a restroom is the issue, then a conversation could be had about the social history of public restrooms and the reasons behind discomfort.
To take CIG as an example, since he offered himself, I realize that plenty of women would probably feel uncomfortable if he were to use their bathroom. Let's imagine the possibilities behind his motivation:
-he's a legit transgender person who just needs to use the bathroom, goes in, does his business, and leaves. There's absolutely no harm here, and any discomfort derives from either socialization or a fear of assault.
-he's a creep who wants to attack or gawk at women, in which case posting a "no transgender allowed" sign (or rather, no one of opposite biological sex) won't stop him. He would be arrested for doing this anywhere, and doing it in a bathroom is actually increasingly risky because there's a greater chance that he could be discovered and cornered.
-he isn't transgender and isn't a criminal, but just wants to ruffle feathers; in which case, again, transgender people aren't the problem--the problem is people who think that transgender people are the problem and they want to make a point, but don't realize they're actually not making a point at all.
Unless CIG intends some kind of sexual harm, or intends to poke his head underneath stalls, what we have is a zone of discomfort reminiscent of the discomfort that white people felt when bathrooms were desegregated.