This is a specific followup to the question 'How would society be different in a world where sex/gender is trivially changable?': in a future (Human, earth) society where (like in the Culture novels), it was an easy, common, and trivial procedure to change sex (genetically, physiogonomically etc), would there still be a distinct trans community with its own identity? I am setting a work in just such a future, and initially wanted to include a trans character, but then realised it isn't altogether clear what it means to be trans in a world where there is no struggle /oppression involved in simply changing one's sex overnight; obviously, the common bond forged by resistance to societal and structural difficulties plays a major part of the trans identity today, as does the common bond of undergoing the often difficult (physically and pscyhologically) medical procedures some members of the trans community use to affirm their gender identity. Would residual prejudice and intolerance still lead to a distinct 'trans' identity? Or, does the ability to change sex with the equivalent of a quick visit to the doctor remove much of the impetus for having a distinct trans identity?
I posit that you are over-thinking it. It seems that you are hung up on the stigma of transgender being the incentive to self-identify.
Step back, and look at all of the things humans self-identify over - hair color (blonds have more fun), bosom size (need I say anything more than 'Bay Watch'?), musculature (jock), financial success (the Club), place of residence (Beverly Hills), the car you drive (Ferrari prestige), military service (once a Marine, always a Marine), college sorority, Alma Matter. None of these are really based on stigma, but they lead to just as much of a sense of self-identity as does belonging to the 'gay community'.
Humans being humans, we will always self-identify by some designation or another, that seems to be our nature. Even if there is absolutely no stigma attached to being 'gay', the fact that it can be defined as a particular quantifiable group of people with the same experiences, group members will self-identify as belonging to the group.
People don't hate transexuals because they are transexuals.
A man transformed into a woman can be either perceived as gross depending on the operation, so basically that person* is not a woman but a guy with boobs.
Or a man transformed into a woman can be perceived as a normal woman... Because it looks like a woman and no one suspects that he is a man.
Some people would still be grossed out to discover they had sex with a woman who was once a man because the idea of having sex with another male is vomit inducing for a lot of men, it doesn't matter if that person* looks like a woman.
It's like asking those people, would you eat bull testicles if they were shaped and looked like normal american meat balls? People would be grossed out anyway, regardless if it's no more a bull testicle.
So until no one discovers that person was once male, no one would discriminate against that person or call that person names like "trap" or "shemale"
For this reason transphobia exists, and it actually only exists for males becoming females..
Like in Afghanistan for example. Female to male is not only accepted but its a widespread tradition
So yeah, not much would change except no one will be saying out loud that they are transexuals.
If transexuality is real and it's something that happens at birth then a baby could simply wish themselves to change gender and never even develop the idea of transexuality. And it would be more of a joke your parents tell about at family gatherings "hey Jerry! Hear that one, did you know George was once a girl? His mother was shocked to find out he grew a penis after changing his diaper"
My best guess is that it would vanish almost entirely, becoming more something like a minor trait instead of a culturally defining item. That's not to say the things that trans people currently do would somehow go out of style, but more that the people who like those things would gather around the specific activity instead of the identity (and would also include some folks who aren't part of the identity, but like the hobby)
A possible comparison might be drawn to a-religiosity. In countries with a high level of religiosity, where people are likely to make a problem about people not being religious, there are atheist communities, where the non-religious gather together to talk about things like science, philosophy, the dangerous of religion, etc. (The US has a fair share of this)
In countries where being a-religious is more then norm, those communities vanish entirely. Without outside resistance, there is nothing to hold them together. The activities remain, but the association with the identity of being "non-religious" stops being meaningful. Then religious people who like talking science join them as well, and they stop being "atheist culture" and just become "people who like talking about science culture".
People feel a need to band together most when they feel threatened by their environment. If you make a problem out of people being transgender, those people will band together and form a sort of culture as a defense mechanism. If you don't care one bit, that need to band will disappear, and much of the culture with it. The parts that remain will be absorbed into the general culture, and at best you might have an unusually high percentage of transgenders within a certain hobby because a lot of them happen to like it.
First I would point out, that the medical possibilities not necessarily cause a change in societal treatment of trans people.
But should that be the case for your setting: I guess there would still be some kind of community, around the shared experience of discovering the differences between ones identity and assigned gender. Sometimes people just want to talk to someone who just understands because of their own experience. Furthermore, even if the transition was trivial from a medical standpoint, I don’t imagine it to be a quick decision (usually). So there could be a community aspect to helping others figure out who they are.
One more thing: It would also be good to consider non-binary and agender people. How do they fit into your setting?
The community would stay, but it's going to be much more diverse and much less exclusive.
Many novel things (cars, planes, photo cameras, surfing, climbing mountain Everest etc.) at first are the domain of a few hardcore enthusiasts which general public might think are crazy and maybe even suicidal. But as the progress goes on, this club of enthusiasts is becoming wider, the associated costs and risk lower, until this activity becomes a mainstream. There's still a community of enthusiasts, but it's no longer small and monolithic.
I am not saying that people would ever be as inclined to undergo a sex change as (for example) an air flight, but general acceptance of it would be much higher.