I think there are some more kind of things that get miscommunicated between the "sides" here, thinking about it.
One "side" takes the stance of people who are gender critical and / or say that a man can't literally become a woman in every way including biological, to mean that they are saying trans people can't don't shouldn't exist.
Speaking for myself, quite obviously trans people exist, it is entirely apparent that they genuinely feel that they are not in the body that they belong in, and this is frequently a cause of massive difficulty, turmoil, leading often to a terrible time and mental health problems and of course people who do act in ways that don't meet gender roles often get a shit time from lots of other people including violence and really serious harm.
The problem for me is not to do with individuals or even trans people as a group getting (correctly) protected in equalities laws and so forth. The problem is when the ability to talk about the people who when they are born everyone says "it's a girl" (or "it's a boy") is removed. And the insistence from some that trans people are literally and in every way the sex they feel internally, and that their experiences growing up are genuine experiences for their internal sex etc. Because then you have to start denying the biological realities of the problems that women face, the actual genuine shit that women and girls get because of their sex, and you get fucked up anomolies which put members of the group previously known as women and girls at risk.
The other thing that bothers me is that any other trans existence is met with such a totally different reaction. Yet a man says "I'm a woman" and everyone is all "yup totally you are of course" what does this say about what society / the world views women as? It's still "not man" isn't it. Was it on this thread or another someone said "what would you call a person who has had the surgery and now has a vagina" and my response is, it's not a vagina. A vagina is a complex organ with various different functions. You can't "make" one. Surgery makes a facsimile of a vagina. This erasure or treatment of women and their bits and bobs as just, well you can make one of those easy, it really sort of undervalues? erm, reduces what we are and what we're made of.
Women's bodies have always been considered lesser, problematical, unmentionable, or as a selection of orifices and so forth. The idea that they are for show, rather than function, all of this seems to support that idea, somehow.
Sorry a ramble there.