non-binary people are still trans

Oh wait sorry I assumed the other inclusion direction, that trans folks are enbies -- it's not what you said, but how I would organise the taxonomy if I was the taxonomy Emperor (which I am not). Though just having three categories (cis, trans, enby) without inclusion relation also makes sense.

category they factually belong to

All categories are man-made. Philosophers and Linguists would have a field day with that one.

Let's deescalate a bit. Anecdotal case, please don't ask me for the source, but once upon a time there was someone identifying as a trans man. Got top surgery. After some soul-searching and being thoroughly dissatisfied with the bottom surgery options available, he decided "aw shucks" and decided to henceforth identify as a butch lesbian, saying "The issue wasn't so much having a pussy but having a dick that's not mine in vicinity to it". Goes by she/they.

Cis, enby or trans? Gay or straight? At which point in time? Snowflake? (well, who isn't).

Stuff like that is why it's important to remember to not make categories normative -- both in the "you are X therefore you must do Y" sense, as well as "If it is bipedal and has no feathers then it's a human" kind of sense (which includes plucked chickens, ask Plato). They are descriptive at best, and noone uses the exact same definitions. Some say that's hot tea, other say it's warm. Do we need to wage wars over that while there's people around who deny temperature?

What happened to "That's, you know, your opinion, man"?