I see it as a tricky issue. The idea that any gender can use any restroom and all of society should have no problem with this.
Me personally, I'd have I think no issue with it, but would likely stick to the same gender bathroom I've always used. If females came in there, I'd admittedly be surprised / caught off guard the first 20 or so times it happens, then likely get used to it. I wouldn't see a reason to discuss the situation and would hope there wouldn't be a need for anyone to have a discussion while I'm in there. Actually, now that I think about it, I'm probably on my 4th or 5th time of it having occurred to me, cause if I go to a place serving alcohol, there's been instances where female bathroom is such a long wait, that a female will come into male restroom to avoid the line. Usually with a boyfriend, but I'm thinking I've encountered situations where that wasn't the case.
But as long as segregated bathrooms are a norm, I think it would be a pretty big deal in society considering restrooms are a place of privacy. The transgender aspect I think helps the situation in the long run, but clouds things a bit in the short run. I wish it wasn't that way, but not sure how reasonable it is to expect it to be different.
Harassment, whenever it shows up, pretty much sucks.