I saw a news story, a couple of years ago, about a new school in Scotland, where they had abandoned traditional male and female toilets, and had instead unisex facilities. The cubicles were all completely private, and there were no urinals, with hand basins in a communal area, and there was an archway out to the corridor, rather than a closed door.
If I recall correctly, the main reason for this change was to try to prevent bullying and antisocial behaviour in the loos - because anyone passing in the corridor could see into the central area with the hand basins, it was thought that this would reduce bullying - because it would be so much more visible.
The reporter spoke to children from the school, and they were all very positive about the new arrangements. They all felt that the cubicles gave them privacy, and no-one was upset at the facilities being unisex - so maybe in the future, that's how all new schools' toilets and changing facilities will be designed.
I have been in unisex 'Changing villages' at swimming pools, too, and I didn't feel uncomfortable.
The question about competitive sports is really interesting and I can see that being problematic, in years to come. It does look as if sportspeople who are born genetically female will be the ones to lose out - and their rights have to be taken into account too. Maybe we will need more sporting catagories - male, female, M to F trans, and F to M trans - we will end up with some complicated system like the one used in para-sports - which does prove that it is do-able.
What would not be fair or right is a system that allows a male sports person to identify as female and then dominate the sport. If the late Jonah Lomu had decided to identify as female, and had joined women's rugby, it would have been actively dangerous for the women on the opposing team, and unfair for the women who wanted to play the same position as Jonah. It is an extreme example, I know.