As a programmer who has done work with databases, it's possible - even likely - that what Iscah says is correct. All of the values that determine your character are stored in a database, and it's quite likely that there are no seperate entries in that database for sex and gender. Dialogue options quite likely look to the same value that was set when you selected your character's sex as the determining value when determining dialogue options. That said, it probably would not be a strain on the system to add an additional database entry for gender, after which a simple search could locate all the PlayerParameter(4)'s in the dialogue text and adjust them to utilize the new PlayerParameter(67) (admittedly a bit tricky, since we're replacing a true/false option with three or more choices). It's not impossible to assume that this couldn't be just as easily applied to other players' displays - after all, when your character information is loaded into their systems, it includes all of the appearance values you've chosen, likely utlizing the same server-side database values that you yourself set when you created your character.

A bigger problem arises when it comes to voiced dialogue that includes gender. While male and female pronoun options are already voiced and available, I'd imagine there's no recorded dialogue with they/them pronouns (or whatever other pronouns you prefer). It would be tremendously expensive to hire all those voice actors to record a third option (let alone more than just a third), and in the cases of voice actors who have passed away, impossible unless you were to recast them.

A further problem appears in dealing with strangers or enemies. Livia sas Junius finds you utterly contemptable and doesn't give a damn what your prefered pronouns are. She's going to address you as prince or princess based on your visible gender alone. Less extreme, folks you meet for the first time are likely to assume your gender based on your visible gender until they get to know you. All this changes the viability of a simple search-and-replace - you need to pick and choose which dialogue branches to adjust, and with so much dialogue in the game this is INCREDIBLY diffiuclt. Unless, of course, you decide to throw reality out the window and decide that everyone in the world magically knows and respects your preferred pronouns without being told - and, perhaps, some LBGTQ folks might be perfectly satisfied with this. It IS a fantasy, after all!

So, to answer the original poster, is such an option available at this time? No.

To address the majority of the thread, is such an option possible? Yes. Is it economically feasible? Possibly, depending on how picky you are. The change is likely not difficult if you're willing to ignore the voiced text, and don't mind total strangers magically knowing your gender identity. Is it likely to happen? Probably not.