“transgender” people aren’t: they’re just crazy. Whittling doesn’t change the wiring of the brain, or the chromosomes. But in principle, such a transformation is possible. It would be an example of real, deep biological change – not the the tinkering at the margins we’re actually on the verge of.
When you think about full metamorphosis in insects, taking a caterpillar into a butterfly, it’s pretty impressive. You wouldn’t guess that a caterpillar and a butterfly were even related – they’re really different. If we hadn’t seen it happen, nobody would believe it possible. Although there are comparable transformations in other species. Sacculina, basically a barnacle, crawls along the body of its host crab until it finds a joint – whereupon it sheds its carapace and injects a microscopic sluglike essence into the crab. It then develops a root system of tendrils , which infiltrate the crab’s nervous system (taking command) and extract nourishment from the crab’s intestine and stomach. The crab is reprogrammed – it looks like and acts like a female crab, but but focuses is efforts into caring for Sacculina’s eggs.
Such natural examples show that really advanced biological engineering is possible, even though we don’t know enough to pull it off yet.
But someday we will. Or any rate we will unless we destroy civilization first, which seems more likely.
Changing sexes (in humans) is not as complicated as turning into a butterfly, but it would seem to require undoing and re-developing a fair amount of brain circuitry. Also changing / redeveloping genitalia, skeleton, muscles, etc. The fact that butterflies can remember some things that they learned as caterpillars suggest this process would be compatible with continuity of identity – so afterwards you would still be ‘you’. Kinda sorta.
Given this kind of capability, changing sex seems fairly trivial. Why not turn into a butterfly? Or considering the square-cube law, a centaur, or a merperson?
Eventually, people would be able to easily transform into a physical form that reflected their true inner nature. I think it’s pretty obvious what that would be for most individuals.