My god this story is silly, just MumsNet stirring the pot to aggravate people. This situation is really no different to single-sex hostel rooms where you self-identify on the website when you book - it can be abused, and if you have concerns that it is, you should speak to a member of staff.
The concern isn't, and shouldn't be, about transgender people - the concern is males who aren't transgender who select female to prey on others. Alternatively, used by males when all the other berths have sold out!
Hear hear, the problem isn't with a certain demographic, sexual orientation, gender etc - it's with people who wish to carry out criminal acts. And as a bonus, there's already a well-established system in place for segregating people who are convicted of criminal acts - prison!
There is a lot of hysteria in general thinking that a certain demographic is going to do a certain thing, and therefore we need to segregate ourselves from them to be safe - see any hysteria over bathroom sharing, "Someone who is X moved in next door to me" etc. In reality though, the perpetrators of crimes call from
all demographics, possibly abusing a certain other demographic by masquerading as them to achieve their objective. That doesn't mean that we need to put in onerous restrictions against certain demographics (who may already be struggling with other things in the first place!), that means that when someone commits a criminal act, they are put through the criminal justice system. It doesn't matter what demographic they might be from - a crime is a crime.
Just as someone might try and commit a crime by masquerading as another gender, there's still plenty of ways they can carry out that same crime without needing to do that. Sticking specifically to the sleeper, they could steal the key/keycard, break the lock, force entry, use date rape drugs in the lounge car and so on... none of those methods are going to be prevented by asking transgender people to provide 'proof' of their transitional status - which as many other posters have explained is not often an easy thing to outright prove. Something that i've not seen touched on either is just how upsetting and insulting it can be to be required to constantly prove you who are. You've lived your whole life feeling like a stranger in your own body, and finally you're getting the help and support you need to address that - but you're having instead to put up of a constant barrage of people saying "I don't believe you, you're not really that, you're really this. Prove it! Prove it! Prove it!". That can be
incredibly distressing.
But anyway, let's keep this simple - let's segregate those who commit crimes and pose an ongoing risk to society from those who are law-abiding and don't post an ongoing risk to society. No need for any of this faff of every organisation having to segregate by arbitrary gender/race/nationality/whatever characteristics.