Factually false. The concept of gender as distinct from biological sex goes back till at least the 1960s, and used by scientists, social and otherwise.
Have a gander at this chart showing the use of the term "gender" in the English language. You'll note it starts to skyrocket up in usage right around the time your cherished (and somewhat obselete) Oxford was printed.
https://books.google.com/ngrams/graph?year_start=1800&year_end=2019&corpus=26&smoothing=7&case_insensitive=on&content=gender
Great. And let's look at the first hit for the 21st century's definition of "gender". Comes from that newfangled interwebs, there, Jehosephat. Oh look, it is cited from Oxford Languages:
Says it all, out here in the 21st century. Please harumph while adjusting the onion on your belt.
That you have to dial the clock back over 40 years makes my point for me. You think you're going to find relevant definitions for smartphones or the World Wide Web in that 1982 dictionary, ducky?
Conceded. You are likely not doing it specifically to be rude. You're just being dishonest, or you don't see the glaring flaws in your justification. Since you keep taking the extra time to snip out my DNA observation, we'll go over it again below.
And the line you are drawing is absolutely, 100% NOT on the scientific, biological sex line. It is absolutely, 100% at the point of convincing presentation, ignoring the scientific, biological fact in its entirety.
Put it to the real world test; you see a trans woman. Looks like a woman, in terms of dress and boobs (that you can't tell are real or implants or a stuffed bra). How do you address them? He or she? Do you demand a genital inspection, or give them a questionnaire about their reconstructive surgeries, presumably demanding evidence?
The scientific, biological reality is their DNA, not having a dick or not. THAT'S the hard scientific line. But you draw the line at their convincing presentation, by your own words.
And as I've said earlier, I don't even disagree with you. But you don't care a whit about the only relevant, scientific, biological fact : their genetic makeup. You care, by your own description, about a convincing presentation. Myself and others also weigh presentation heavily, but we are not requiring them to drop trou before we call them a "she". If they can't afford, or have not yet reached the point of the slice and dice, that's okay with me. As I said earlier with "Babette", it took me a while to not see a man in a dress. But I fully acknowledged her as a legitimate woman before she even got her implants (and no, I've never even asked if she got the Johnson cut off, because it seriously doesn't matter. I'm sure she did if she could afford it, but it is not the "line drawn" of her sincerity. She already demonstrates that.