You're right. The Charlotte ordinance allowed transgender people to use either bathroom they want. The addition of non-gender restrooms was proposed as an alternative for those who don't want men in the women's bathroom.
I have a serious question. How do we know if a man in the women's bathroom or locker room is transgender? How can you identify a transgender vs a pervert, voyeur, or teenager w/ raging hormones & curiosity? What would stop any man from walking into the women's locker room just to look around, and claim he was transgender if challenged?
Another serious question. How do we weigh a woman's right to privacy against a transgender's right to use the women's bathroom? Is there no solution where one right doesn't negate the other?
Those are good questions, and I don't have answers to them right off the top of my head. I would only point out, as others have done, that it looks like transgendered people are far more often the victims of assault than vice-versa, and this looks to be what prompted the non-discrimination law in the first place. As I have said, as far as I know, transgender people have always used the bathroom of the sex they identify with. The non-discrimination law codifies that, and in this sense it is almost the historically conservative position here. I don't
think the non-discrimination law is mere provocation by liberals who are trying to bolster their progressive credentials. There are too many stories of transgendered people who have been victims of attacks for that, from what I can see. I would say if the non-discrimination law becomes a problem for the reasons you pointed out, it should be altered or amended. On the whole, I think North Carolina's legislature are the ones doing the ideological grandstanding here.