But I recognize that such ideals haven’t really succeeded in western society; so maybe it’s easier to wear what you want as a particular traditional gender that you pick. And that’s really just another way to look at the same thing. And maybe society understands that more?

I don’t speak for everyone but I think for some people this is a big part of it. Fighting for what you just described here is hard enough already. Many people just want to live their lives and be happy. Also, non-binary people exist and are generally considered to be a part of the trans umbrella. I think the first step to building a society where gender truely doesn’t matter starts with building a society where all trans people are welcomed and accepted.

In addition to what others have said, I’d like to add a little more information.

Hormones work by changing your gene expression. Every one of us has all the DNA for both typically male and typically female traits. Hormones play a part in deciding what parts of your DNA are active within your cells and what parts aren’t. There’s a complicated set of interactions that decides what hormones you produce naturally and how your body responds to them. Sometimes something happens in an atypical way with that complex set of interactions and that’s how intersex people exist.

(There are examples of people with XY chromosomes who have internal testes but are insensitive to testosterone and grow up female, and even examples of people with XY chromosomes who have functioning uteruses and have given birth naturally. It can get very complicated)

When you go on HRT as part of a medical transition, the instructions your cells are following in your DNA switch to the instructions tied to those hormones. That’s how trans people’s bodies change. Their cells are actually functioning differently.

A trans women on estrogen for a long enough time will eventually have their blood proteins go to a more typically female profile. They’ll also see their risk factor for certain diseases switch. The risk of cardiovascular disease goes down (typically something that affects more males) and their risk for autoimmune disease go up (typically something that affects more females).

So are trans woman biologically men? Eh, not quite. Saying somebody is biologically male/female is a little reductive. It can be complicated.