Non-binary seems like it could have several non-compatible meanings, so I wanted to list some of those meanings and see if there are any others out there I don't know.
One way I could think of non-binary is as being a kind of third gender category, like there are men, women, and non-binary people. In this sense of non-binary a butch woman who considers themselves a woman would not be non-binary because they are a woman.
Sometimes non-binary is used like "genderqueer" is sometimes used, as a generic description of anyone who doesn't fit perfectly in the narrow confines of the binary genders (i.e. men and women). In this sense a butch woman could see themselves as a woman, but also as genderqueer and non-binary, as they do not conform to binary gender norms for women.
Another way non-binary seems to be used (related to genderqueer in its historical context) is as a political term, an identity taken up by otherwise cis-sexual and even cis-gendered people who wish to resist binary gender norms and policing. In this sense even a femme cis-sexual woman might identify as non-binary. Sometimes this political identity label might come with a gender expression that cuts against the gender expectations for the assigned sex at birth, but it doesn't have to. (I recently met two people whose gender expressions matched their assigned sex at birth but who identified as non-binary in this political sense.)
I was wondering what other meanings of non-binary are out there, and how they are commonly used.
Note: gatekeeping what is "really" non-binary seems pointless to me, since I agree with Wittgenstein that "language is use".
I know people get heated about policing what a word means (and I am guilty of this myself), but in the interest of inclusion, pluralism, and general cooperation in our community I think we can find a way to communicate with overlapping and different meanings of a shared term.
Interesting, so there is this notion of non-binary as applying a spectrum to previously binomial things, like sex, gender, and sexuality.
It's also interesting that you position non-binary less as a label or identity but more as a fact about someone (that they may or may not know, or identify with). For example, a trans woman who does not want bottom surgery is considered less feminine, then, on the spectrum.
See, I wonder if you couldn't take the same distinction and apply it to even more refined categories. I think of Helen Daly's paper "Modelling Sex/Gender" (PDF), in which Daly proposes a "many strands" model of sex and gender, whereby sex or gender is not thought of as a set of categories whether binary (as man or woman) or ternary (as man, woman, or non-binary) nor as a spectrum between two extremes (man on one end, woman on the other, and "non-binary" being anything in-between), but rather as a set of characteristics that may be spectral or not.
This is suggested as a way to help policy makers navigate the complexity of sex/gender, for example when deciding whether someone qualifies to compete in men's or women's sports.
Personally it seems this thinking ignores the potential for policy makers to have a transphobic bias when choosing relevant characteristics to include in defining someone's sex or gender for the sake of a given decision, but what I do like is that it does give a helpful model for approaching contextually different notions of sex and gender.
So in a medical context a doctor could use the many-strands model to approach better care for their patients. Rather than focusing on whether a patient is a man or woman, they can focus on facts like whether a patient has a prostate or not, whether they have a uterus or not, etc.
So the question comes back that in what context would an otherwise binary trans woman need to be labelled non-binary for being no-op or pre-op?
The label can function various ways, but there seems to be something wrong with labeling an intersex or trans woman as somehow less feminine or less of a woman due to having the "wrong" genitalia.
I think this intuition probably comes from the weight we give to someone's internal sense of themselves, and that the brain and mind are the ultimate authority of who someone is and what their authentic identity is.
Anyway, I know you weren't attempting to foist the non-binary label onto binary-identifying trans women, but I'm thinking about the theoretical limitations of a model like that, which seems to impose that kind of meaning onto them regardless of how they experience gender.
I could also be wrong about my assumptions, I admit there might be an empirical aspect to these questions that is being left out (as dangerous or politically unsavory as that kind of biological determinism can be).
I think the whole benefit of a non-binary system like this would be that we see people less as labels such as man or woman, which many struggle to fit into, and more just as a person. Everyone has their own sexuality and who they're attracted to anyway and that won't change based on this. The only difficulty I could see here is that the question of genitals would obviously be blurry since we don't present them openly, but I'm sure that can also be solved in an elegant way without giving anyone a bad surprise.
Medically when it comes to the biological sex & identification I think we could just as well use XY chromosomes in identifying documents like passports, IDs, etc. That does the same job and is generally more neutral.