Oh.... no....
You see, when it comes to things like cross dressing or gay marriage, those things are choices, and I would go on record saying that most gamer's and even just people who actively play XIV and not many other games, would respect others choices about their own lives.
When you decide to put in something such as a non-binary gender, what you're providing isn't a choice, but a statement. It's a statement that says "my version of reality is correct and yours is not".
It's one thing to have in a fictional universe as a matter of creative effort, and another thing entirely to have as a matter of political recognition or real world acknowledgement. I can think of one story in particular in which humanoid beings are capable of fluctuating between male and female as they wish with scientific principal to back it up, and that was acceptable as it had no reliance on the real world to make it such a plot point.
I play as myself in XIV. I named my character after myself and modeled it after myself. I can understand the desire to do so, while I doubt you've actually put effort into doing the same I recognize the lack of satisfaction in never being able to do such a thing. I play many games, and in most of those games I am unable to model or name my character, and at those times I take the perspective of the character that I'm playing rather than myself. I would suggest that you do the same in this regard. Playing as yourself is not the ultimate goal of video games, experiencing what you can't experience in the real world is much closer to the ultimate goal.
I share the same sentiment as some others here as well. Frankly put I'm sick of politics as a whole. I spent way too much of my time on it within the last couple of years, that at this moment in my life I want to escape from it, and FFXIV is a good way for me to do that. I'd really rather FFXIV not be infected with politics like that. The "option" you present for us is the exact opposite of an option for players such as myself, which I assume constitutes many more people than what would accommodate for the "choice" that you provide.