I believe trans women are "real women" in just about every way that matters. I only make an exception when I absolutely have to. For example, in sports, or in a medical context.
It might help to remember the word "women" is just a label we assign to people who share a certain common set of social and biological traits. And the majority of these traits trans women share, however in the case of trans women there are some exceptions. But it's not just trans people who don't fit cleanly into these groups, there are similar difficulties to be had with intersex people for example.
There are no easy answers here. Life isn't black and white. It's silly to think we can cleanly divide the whole of society into to clear categories.
The way I read it is that it's taken over 50 years for "gender" and "sex" to become different things. It's still a word that's transitioning (ok, some pun intended), but essentially we're past the tipping point now and you'll offend people if you use gender words incorrectly.
The WHO has the progressive definition that you want to be using: https://www.who.int/gender-equity-rights/understanding/gende...
This is in contrast with the dictionary definition from Google, which still uses biological sex: https://www.google.com/search?q=define+gender
It does feel a little bit like when "literally" changed meaning to "figuratively", but this distinction is really important to an ever growing group of people.
It's also worth noting that it applies to gender words like "man" or "woman" which are different than sex words like "male" and "female".
I still don't understand how non-binary people fit into this, but if you embrace the "singular they", you'll probably not offend anyone.
N.B: what somebody says they are banned for and what they were actually banned for often differ.
Based on our experience at HN (not that it generalizes) I'd even say they usually differ.
It's not a matter of "my side has facts and your side has opinions." It's that we disagree on what the facts are. You can find a lot of scientists from a few centuries ago confidently asserting that black people are subhuman. It doesn't magically make them not-racist because they believed it to be a true fact.
They were wrong, and you are wrong.
Don't forget things like androgen insensitivity syndrome, infertile women, etc.
If we want a simple inclusive definition, you can't beat that.
My problem isn't with your definition, it's with your implied assertion that we should "we want a simple inclusive definition," which is clearly not the case, as the differing priorities in definition are literally central to the debate.