No problem! More than happy to discuss things.
Will preface by saying that things I say here are my own personal opinion that may or may not be reflective of the general feelings, but I can't claim to speak for all trans people.
It's my impression that trans people typically have a strong aversion to being called "man" or "women" on the basis of sex as opposed to gender. Yet I don't sense as much of an aversion to terms like "assigned female at birth" or "assigned male at birth."
Primarily because what some doctor defines us as the second we come out of the womb is not only obviously outside of our control, but it's also long before we have any real concept of self, so who are we to say that, from the instant we exit the womb that we aren't male or female? Given the population of people who identify as trans vs. the rest of the general population, doctors are right more often than they're wrong in terms of relating sex to gender, so they're just doing the best they can.
Sex isn't strictly binary, but with the exception of intersex people, you can generally categorize people in to groups of mainly having female vs. male sex characteristics (to my knowledge, trans people don't really dispute this). More so pre-op vs post-op, but the point is that one could select some group of criteria they are going off of and then categorize sex based on that. It's kind of an arbitrary thing to categorize people off of, but so is the amount of melanin in one's skin, or how tall someone is, or the color of their hair. And it's still common to use words like "red-headed" or "tall" or "black" to describe people. Or even age, which like sex isn't easily observable but you usually just take someone's word for it.
Correct. The problem lies in that people who tend to be anti-trans then take those sex-defining characteristics and conflate it with gender (i.e. you have penis, therefore you are guy) which isn't really how that works. Even categorizing people by sexual characteristics gets tricky if we were to include populations like intersex people (you were excluding them to make your statement, but even without them how does one classify a girl who lacks ovaries or a girl who possesses testes?)
So my question is: in your view, with regard to misgendering, is the aversion to sex categorizations being made in the first place, or just the terms "man" and "woman" being used? Like if people started using the terms "blargh" and "zog" instead of "man" and "woman," and blargh and zog referred to preponderance of particular sex characteristics, do you think most trans people would still be opposed to that?
It's not necessarily just strictly categorizing things by sex, though. Rather, it's conflating sex with gender that is the primary issue. If we wanted to specifically look at categorizing people by sex, I suppose you could say something along the lines of "Everyone who possesses a penis stand over here and everyone who possesses a vagina stand over here" (again ignoring intersex people for the purposes of the example), and (again, can't really speak for every transgender person out there), I don't think the average trans person would have too many issues with that (outside of general dysphoric feelings). That's strictly where that categorization would have to end, though - the second you try to go further than that is where misgendering typically begins. And given most people seem incapable of stopping there, that's where the issue lies most of the time.
So I guess to directly answer the question: If you wanted to replace penis with "blargh" and vagina with "zog", theoretically I don't see too many trans people having issue with it. In reality, though, it'd end up just being the new medium through which people conflate sex with gender, so it wouldn't change much.