Prefacing this by saying, I acknowledge at the end of the day, it's your game, your call and I'll respect that.
That being said, while I get what you're saying, I don't necessarily agree with your reasoning.
Mainly just that like, the detail of whether the MC is cis or trans doesn't seem that relevant, so leaving it ambiguous doesn't really affect the story much. Like yes it's ambiguity, but in my opinion at least, ambiguity only becomes an issue if it's ambiguity that obfuscates important information from the reader. There are plenty of other things the story keeps ambiguous about, simply because those details aren't ever relevant. So I really don't see how the ambiguity is unfair to the reader in this one case.
Like if it were plot relevant what the player had in their pants, or the game went in depth about gender, gender roles and the like, I could see that. But as is, it seems like the details mentioned (i.e. not questioning gender, specifics of what happened) are kinda superfluous, and as demonstrated by the nonbinary option, can be side-stepped without much consequence.
On the other hand, by not by no having that ambiguity, the game is excluding binary trans identities it otherwise wouldn't be, which is arguably unfair in of itself, and will possibly put some readers off. Meanwhile, most people probably wouldn't give it a second thought that the game doesn't explicitly state whether the MC is trans or not.
I know the sex scenes do complicate this a bit, but that would be pretty easy to solve by just tweaking them a bit (like, I've only played Ferret's sex scene, but literally the only tweak they'd need is just removing "another" from the line, "...another woman's breasts..." in the female version.) and then just having the player just like pick what's in their pants and play that version. Side note, this would also fix the issue I came across replaying as a nonbinary character, where it just uses the female version which besides just misgendering the player (see the above line about breasts) kinda plays into some negative stereotypes about nonbinary people by just assuming they're AFAB.
Again, it's your game and your call, but I do hope you at least consider it, because I very much feel like the positives of adding that ambiguity outweigh the negatives.
Though if you do want to keep it specific, I will also say, that irrelevance to the overall story is kind of a boon when it comes to adding trans options. Like there's only a couple places, where I really felt like it'd come up.
1) Obviously the gender choice itself. Just the line about not questioning your gender could be replaced with something like, "You'd known for a while that you were not a man/woman like everyone had said you were. Though this was considered strange, the council ultimately didn't care as long as you still took your turn in the chamber."
2) Maybe some line mentioning it when doing the childhood friend reveal with Heron, or the reveal with the MC's dad.
3) When talking to Robin in Chapter 7, just have the same line about knowing how they feel, that comes up if the MC is nonbinary come up. You could maybe modify it a bit to be like, "I can't say it's exactly the same for me, but I still have an idea of how you feel."
4) For the sex scenes, see the above part about them.
Anyway sorry to keep pestering you on this. It's just I really like the game otherwise, and so I feel like this is like the one thing holding it back for me.