Transitioning isn’t to magically become the other gender, it’s to become something more tolerable, and more expressive of ones individual self. It’s not to convince cis people either. Many trans people have friends and date exclusively in the LGBT community, while they want to be addressed in a way they feel pertains to them, they’re not trying to convince the whole world.
The human body starts with only the slightest lean of sexual characteristics, deciding the penis or vagina, then the body actively grows based on whatever primary sex hormone dominates.
Male to female for example, with their hormones altered in favor of estrogen, they will gain the female primary sex characteristic of 30% more body fat, especially in the breast region, their voice will even lighten from their thyroidal cartilage losing density (though it won’t get much smaller) their epithelium will become softer, and facial hair will slow down/cease.
A female to male hormone therapy will result in emergence of facial hair and the primary male characteristic of 50% more upper body muscle.
These hormone treatments aren’t to convince everyone, many trans people consider themselves to be in a different category than cis people, and often date in this category. They don’t care what you think. As for bathrooms people just need to learn to piss and shit without making it a sexually charged issue, but because cis males are so rapey, mtf often don’t feel safe going in the male bathroom.