Not convincing? That’s your problem, not everyone else’s.
The entire silly debate over who is allowed in which sex’s facilities can be solved by the simple rule that if someone is a woman, or seems to be a woman to all other women, then they can use the women’s. Likewise, if someone is a man, or seems to be a man to all other men, then they can use the men’s.
After all, for all everyone who has ever used public facilities can know, they have already been used by someone of the other sex but who was not distinguishable as such. If you never noticed, you can never know.
So genuine ‘trans’ people who were born one sex but live (not just pretend occasionally) as the other, will have no problem. If someone truly has converted from male to female in all aspects such that nobody could say they ever were male (or vice-versa), what’s the big deal .. indeed, how can there be a big deal given that nobody will be able to tell?
So that leaves those who see themselves in a way that other people do not. To them, I say, you have the problem, not everyone else. While I might sympathise with your problems, don’t try solving any of them by making the rest of society conform to your delusion. When or if you can make your delusion into an illusion that everyone around you believes in, then you will have solved your problem.
Footnote: I like to see myself as a multi-millionaire. Unfortunately, the benefit office won’t conform to my delusions – despite the mental trauma that not being a multi-millionaire causes me – and the car dealer won’t lease me that lovely DB9 I want. I guess I’ll just have to make myself into a genuine multi-millionaire to be properly convincing. That will show them all.