I HATE the argument that you shouldn't do stuff because it might make other people feel slightly uncomfortable for a few seconds. It's like the argument against gay marriage. I feel uncomfortable when dads take their young daughters into the men's toilets, but I understand that, for them, it's a choice between doing that and sending them alone into the women's toilets which is just not something that most parents would do.
If you are born as X but identify as Y, you have every right to use the Y toilets. End of. Especially as you'll most likely look like Y anyway.