I might be wrong, but I think there's currently a gender variable both in the soul and the body. But we haven't really addressed what differences mean, since it doesn't generate trans people (if that's the right model for it), and there are no soul swapping spells. I don't think it's a straightforward implementation, overall -- trans characters in games generally lean on the fact that their in-game societies also have strong gender norms, which we don't have in DF to any meaningful degree (eg, gender-restricted clothing etc.). There's a sort of trans-erasing assertion sitting there, which is bad (ie, it asserts trans people don't exist without such norms), but I think it's complicated to sort out the way things are structured, and I don't have a clear road forward (eg, how do we handle pronouns in the heterogeneous body/soul case without it looking like a simple bug to report -- the character needs a larger world model within which to state their identity). The first chance we'd have is with the status groups after the myth release, though basic soul swapping/stacking/merging/etc might happen earlier.
I don't know if this is a can of worms that should be opened, wheter for realisms sake or otherwise - especially since, as you said, it wouldn't make sense in the current setting which has no sexual dymorphism or gender roles.
I admit if this was added alongside dymorphism, "castes" in the traditional sense of the word and not the in-game one, gender roles, gender expectations (clothing, behavior, etc.) and so on it could lead to a lot of interesting interactions on the internal workings of cultures. I.e having one dwarven culture only accept queens, but her only heir being a male it'd cause the local nobles and court to be displeased, creating complications, or a human civ only having female priestesses in their temples, who also get certain privileges due to their role, or another civ having a military caste consisting entirely of males, etc. etc. Then there's breaking of traditions and so on leading to other dynamic changes - the whole thing just gets more complex and in-depth from there.
However, on its own, I do not see what the addition of trans people would add at all to the game. I don't like politics of any sort in games, wheter right or left, but with the issue having been so heavily politicized in recent years (and with you yourself saying you didn't add dymorphism in order to "not upset people" - a trap a lot of game devs have fallen in already) I cannot help but feel highly skeptical and mixed towards this.
My main message regarding this though - if you want to have the game be realistic, then adding in the nastier parts of realism and history that people dislike - prejudice, dymorphism, gender roles, and so on - is pretty much required. Most fantasy games already do this, and its not like the playerbase hasn't done their fair share of atrocities - compared to outright mermaid genocide I'd say prejudice or dymorphism are both rather tame.