Hi Pinot, welcome to FWR.
There is some confusion with terms. The words sex and gender have been used interchangeably, despite them describing different things.
Sex is a biological and immutable thing. Human beings are a broadly sexually dimorphic species of mammal. That is, there are two sexes, male and female. It is impossible to change sex, it is written into the very core of our bodies. People can take hormones and have surgical alterations to their bodies, but will remain their biological sex for ever. In 200 years time, if archaeologists dig up a transwoman's skeleton, they will know, from biological markers that it was the skeleton of a male human.
Gender on the other hand is entirely societal. Women have no innate desire to care, empathise, nurture etc, they are roles that society imposes and reinforces on females from before birth. Men are no more innately scientific, dynamic, unemotional etc than women, again, these are characteristics that are imposed on males.
These gender classifications become problematic when they are rigidly enforced or expected. Boys who are emotional, caring, empathetic might get told that they're 'acting like a girl', girls who similarly behave outside of rigid gender norms might be called tomboys, or told to behave in a more ladylike fashion. And this can cause huge confusion and upset to the child, which can lead to them wondering if maybe they have been 'born wrong'. Hence transing.
Transwomen will always be biological males. They may present as a facsimile of a woman, but because they have not had the years of having 'female' acceptable behaviours reinforced and 'male' acceptable ones disincentivised, they really don't have a clear idea of what 'being a woman' is. Instead of trying to force women to accept them as women, transwomen might be better served in the long run in destigmatising the expression.
The majority of transwomen quietly get on with living their lives, however, a notable minority of them seem to spend an inordinate amount of time posting all over fora/Twitter/Facebook demanding validation from women of their womanhood, which strikes me as deeply unhealthy for them.
The word appropriation does suggest a malign intent, and I don't think the majority of transwomen have that. There is a subset of people who call themselves transwomen who are what is known as autogynephilic. They get a sexual kick out of wearing women's clothing, and are no more trans than my desk, I would say that what they do is appropriative, in that they do set out to act out a highly sexualised persona of femininity.
LRD is correct when she says: I think, broadly, that being trans is one of the many ways people have of trying to cope with the absolute absurdity of patriarchal gender roles. Where I diverge from some (not all) trans people, is that I think if we could only get rid of 'gender' as a concept, we would probably not need the concept of 'transition' either.
Without rigidly enforced gender roles, men and women would be free to be human beings in all the many different ways that's possible, without labels or stigma. And that would be an ideal world for everyone.
I hope this makes sense, I kept getting distracted! (it's also taken about an hour to write it, so the thread has no doubt moved on!)