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.
Firstly, "transgendered" isn't a thing.
In the same way that tall people aren't "talled", trans people aren't "transgendered". It's not something that happens to us, it's who we are...
As for your question though, what you're describing is being closeted. A queer person who isn't able to live authentically in their daily life, who has to hide a part of who they are, is closeted, and that's what you're describing in your question. It has nothing to do with gender. Unfortunately, every part of the LGBTQ community has members that have to be closeted, even today...