I'm currently in LoC, the bit where Egwene is raised to the Amyrlin Seat - which involves all Aes Sedai present having to strip to the waist to prove their womanhood. That part definitely had me thinking the same thing, and it's far from the first time.
I have the same impression - it's not so much a question of good guys or bad guys, as a question of people from the present day vs the survivors of the previous Age, who as it happens are only the Forsaken.
But the fundamental and very binary difference between saidin and saidar is something of all Ages, I guess - which is definitely a major obstacle not just for trans people, but for anyone who views gender as not or not entirely binary. The Third Age social views reinforce the same point. And while they could play down the latter, it's hard to see how the TV show can play down the binary saidin/saidar split.
Of course, once you start paying attention to this, you'll find most fantasy that wasn't written in the last decade or two problematic, with some mostly female exceptions who were paying particular attention to gender. If you read Tad Williams' books, first his original Memory, Sorrow and Thorn trilogy published in the 80s and 90s, and then the sequel series The Last King of Osten Ard, first book published in 2017, it's a great way to see how fantasy has evolved in that time, in a number of aspects including gender, less black-white morality, more racial diversity, more different viewpoints, and so on.
By the standards of the male fantasy authors who had gone before him, Jordan in WoT is really very good at writing credible female characters, despite the infamous sniffing and the reverse sexism you mentioned. And based on what the series suggests about his personal views, you can't say he was socially conservative, for a guy of his age... but he definitely did see male/female as a binary and made that a key part of the series.