Among the many issues posed by the wider acceptance of rights of transsexual persons is that of the gender-segregated bathroom, and who goes where.
I have been thinking about this for some time, ever since some of our favourite restaurants did away with men's and women's bathrooms in favour of one (single occupancy) room. I always felt a slight squeam factor in those, as the previous occupant all too often did not "aim to please". Sure, I've been in some messy stalls in women's bathrooms, but by and large, women can be counted on to operate within the confines of the porcelain.
Once a person chooses which door she'll push, based on how she identifies, the important thing is to conduct ones' self efficiently and neatly. I have seen a real erosion in this civility, with litter (and worse) left on the seat and floor, and even deliberate vandalism that requires a cleaning crew.
I've read that some women fear men will enter under the guise of being trans, but are actually male voyeurs. Some of the persons I have met at the sink have been nearly impossible to identify as male or female, but they have conducted themselves entirely appropriately. (And we know that abuse and violence are overwhelmingly committed against the trans person.)
The person in transition cannot always find a single-use facility, but perhaps, in the early stage where she might still be read as a male, she could go in to a multiple-use bathroom with a woman friend. A practical solution would be for her say, "I'm a woman, don't worry!" but that may be asking a lot.
In Canada, a forthcoming government bill will add gender identity as a prohibited ground for discrimination under the Canadian Human Rights Act, and trans persons will be protected against hate speech under the Criminal Code. Though in the past a similar bill was defeated in the Senate, Prime Minister Justin Trudeau said, "We can and should do more", and politicians formerly against have changed their position.
As we find ways to integrate persons formerly forced to live in shadow, we must thoughtfully dismantle barrier after barrier. You could say it's a process of elimination.