You are mislabeling them and shoehorning them into Transgenderism when they aren't transgender.

Okay, fine. That doesn't answer the question though. How do you accommodate someone who doesn't believe gender exists? I've tried looking into actual literature on the subject since I did the survey a few years back, as the weird backlash I received created the curiosity to look into a subject I apparently didn't know a lot about. What I found is more tied to the frustration I'm conveying right now, as that's where I've ran into explicit arguments and assertions beyond merely that some people do not identify with a gender; it's the stronger claim that neither sex nor gender has a solid basis for everybody else.

I wasn't frustrated with the students I surveyed, I was fascinated that asking people to anonymously and optional specify their gender was seen as problematic by some students. I'm not frustrated by how anybody identifies, how they view themselves, what a person feels is right is right in regards to themselves and I'm in no place to challenge that. That's exactly why I didn't dare strike an attitude toward the students who challenged that part of my survey. However, the deeper I get into the literature on gender, sex, and identity the more I find myself frustrated. Not at how individuals identify themselves, but rather at claims, such as not believing gender or sometimes even sex exists, is accepted with a straight face. It's true that we're speaking of an issue that is comprised of very complex biological and social cultural components, and I wouldn't dare think "oh, you think you're genderless but you're not". But to make the reverse claim, like "you think you're a woman but you're not because gender isn't real" is pretty absurd.

Looking back on my experience with those particular students, it does not feel so absurd to assume, even if they didn't explicit state it, that a few of them didn't believe in gender. Maybe I'm wrong to assume that, but given their academic background and likely curriculum there's a chance they were at least being exposed to such ideas about gender. Again, how a person identifies is not for me meddle with. I did my best to accommodate people who identify outside of a gender binary, and I even made the suggestion that the question could be skipped. And yet I feel like the third option you initially brought up, the option I used myself to recognize that not everybody identifies with a binary gender, isn't good enough of a solution. Apparently it still pisses people off, apparently people will argue with a straight face that gender does not exist and that's why questions like mine are problematic. There's identifying as genderless, which is a thing that I can wrap my head around, and then there's the ideological denial of gender as a thing that exists, which seems pretty incomprehensible. I know how to respectfully acknowledge people who don't identify with gender at all...I frankly do not know how to be faced with the claim that gender isn't real and think this person has some pretty ridiculous ideological stances.

And on that note, the more I read into literature about trans gender issues, gender identity, and the like, the less I know what the word transphobic means. Can you even be considered transphobic if you have a discriminatory attitude toward people who don't identify with gender at all? I'm pretty sure that would be the word of choice regardless though since there's no other popularized word to take its place in the context I described. I used the survey I did as starting point because before that I didn't even realize gender denial was a real ideological stance taken seriously. I did my best to accommodate and try to be inclusive, it turned out that even adding a third option, like you initially mentioned, wasn't enough to make EVERYBODY happy, nor was the subtle 4th option of leaving it blank. It wasn't good enough because I still received negative feedback from those students, and while I continue to search for a solution by reading into gender issues literature, it's quite clear that it's not quite clear how to please some people.

I feel like you are still leaving information out of your anecdotes, at first it sounds like you are surveying people in a classroom, now it sounds like you stood outside and flagged people down to take a survey. Two every different contexts, students are a lot more likely to mess with a random guy asking survey questions than a in class survey.

Mmm, no. I never stated that, and I don't know why you'd assume that professors would let people satisfy what amounts to idle curiosity coming from another field with their own class time. Even if I was a member of actual faculty, I couldn't just hand out my own survey to students during scheduled class time if it wasn't directly pertinent to that particular class or lesson; that would be unethical. The survey was distributed in two ways: For the classes I personally had on my schedule, I asked for permission to ask students if they would like to fill out my survey before or after class, which avoided disrupting the class. In other cases, I asked deans and secretaries in charge of particular areas of campus I wouldn't normally have any reason to be in if I would be allowed to hand out my survey either in a lobby or directly outside of the building. It all had to be anonymous too, and without an IRB signature slip for all 307 of the surveys I cannot officially publish my work either.