Trans people exist in the real world, but I think our contemporary conception of "gender" and thus "transgender" doesn't necessarily exist in fantasy worlds. It's kind of a bugbear of mine when it comes to fantasy, where they just assume that because the society has both men and women it also must have developed the works of Judith Butler at some point.
This is an interesting thought experiment but utterly pointless.
Gender exists in D&D worlds in the exact same way every other word we use in D&D games does. If a player plays a transgender character, every term they use to describe it exists in that setting along with that character.
We don't have a separate idea of what gender is as a concept just because we're playing D&D in the same way we don't have a different conception of what "Gay" means or "Wife" or "Trade Route".
All of these things are specific terms which bear cultural weight to us that wouldn't to various peoples in various times. And because we are imagining them into the game world, they exist in the gameworld with those cultural expectations.
Judith Butler doesn't have to exist for that to be a thing. Just like a complex legal system around various degrees of murder or sexual assault don't have to be written for a campaign setting for us as players to call those things immoral or illegal and present consequences for those actions.
We impose our modern ideas upon the game world in a million minor ways. Why does this one have to be special?
Like, take the Thai "kathoey" or "ladyboy". It's a real, extant gender expression that is either outside of or between the cisgender identity as it is known in both western and Thai culture... but "kathoey" do not exist in American culture, and in an American context they would be pigeonholed not into "cisman" or "ciswoman", but "transwoman" or "nonbinary", which do not exactly encapsulate the specific cultural experience of that particular gender.
Okay. So. If you're ready to develop an entire concept of Gender for every culture in a campaign setting that doesn't align with the real world conception of it I might be willing to run with it for a game or two. Maybe more if the setting is captivating.
But the setting where that is a thing doesn't exist. And thus we impose our personal perceptions.
I think it's right to assume that non-binary genders exist in all cultures, and that it is possible to move between one or more of those genders, but I don't think calling these genders (or characters with these gender expressions) "transwomen" or "transmen" (with all the cultural baggage they entail) is necessarily appropriate, unless the society in question is specifically based on that of the 21st century west.
When you develop period and setting-specific language that encapsulates the idea based on the in-game cultures and then convince the other people at the table to use that language and understand it... Bully for you!
Until then, people are just going to use the language they have and understand in order to communicate ideas to the other people around the table. Because that's all that really matters when we're using terms like this: The ability to communicate concepts to each other.
Alternatively: You could pretend that while your players are saying "My character, Eliza, is Trans" that they're actually speaking elven and saying "My character's identity has passed with the phases of the last moon and is now known to all the trees of Lothlorien as Eliza, daughter of the changing waters" in the elven tongue or some such.
Fantasy writers should be coming up with new genders just as readily as they come up with new races and new languages. It's kind of like how you can have a dark-skinned character with tightly coiled hair and call them "black", lowercase, but not "Black", uppercase, unless that ethnic group was specifically subjected to similar historical forces that forged "Blackness" in reality (IE, triangular trade, mass slavery, colonialism, etc) they're about as "Black" as they are "Indonesian" or "Catalan."
It's nice in theory... but races have mechanical aspects which is why people invent new ones at a vastly accelerated rate, now, than they ever did before.
Gender probably shouldn't have comparable mechanical aspects. Which makes it way less 'Interesting' for game designers to fiddle with. Meanwhile campaign setting writers are more interested in writing about threats, locations, individuals, languages, etc. And our modern language covers things like gender and transitioning so it's rarely mentioned aside from "This is a thing that sometimes happens" or "NO TRANS RACES ALLOWED" if you're a rampaging douchenozzle setting writer...
Give it time. Language changes. While Trans and Transgender are all the rage, now, due to the urge to medicalize people like us, language will shift to be something you might find more palatable in a fantasy setting.