And yet there clearly are extremists - on both sides.
From transwomen are just men, sit down and shut up, to my personal gender identity is all that matters and I should be able to walk into a chemist and demand copious amounts of free hormones.
I think the problem is that recognising trans identity as valid is pretty much step 1 and if you can't get to that point then there is little conversation to be had beyond that. If that point is being staked out as the argument's middle ground then I think that only shows the problem.
I mostly agree with this post, but I would add a caveat. I think that recognizing trans-identity is an important step. But I don't equate that with saying that the term "women" applies to them. (Please note, I'm also not saying that the term does not apply to them.
Now,hear me out....
(Sorry, this is going to be long. One of the reasons I don't post a lot is that I tend to go long and over-explain and/or over-account for counters in the name of completeness.)
For me, it's just a term. Same with man. I don't have an attachment to the term where it represents the experience I've lived, a centuries old struggle against oppression or a sisterhood united by biology and experience. (That's probably an inadequate description, but I'm trying to describe something I don't fully understand.)
But for at least some of the women in the world, there is a huge investment in that term. To them it represents all their experiences, which they closely tie to biology, which they see a huge factor in their daily lives, both social and otherwise. (Again, as a male, I don't see my biology affecting my daily choices and identity in the same ways or magnitude that it seems to for women.)
This combination of social and biological experience forms an identity they call women. You refer to it as cis-women. As you can see, some women are resistant to changing the name of their identity. when someone comes along and wants to change the term for the way you think of yourself (your identity) you are likely to resist that. This is especially true if there is a lot of emotion and pride invested. Such as that of a group that has been oppressed for thousands of years, and while still disadvantaged, has clawed their way to the point where they are finally seeing daylight. And yes, a lot of the people for which this is a big issue will be the ones most active in their struggle: feminists and radical feminists.
If you leave the terminology at trans-women and women, I think you will see acceptance that trans-women's experiences are valid, that trans-women is a valid experience identity.
Which is, as you say, step one.
But it seems that some people have tied that step to the redefinition of "woman" to be, instead of an identity, to be a set of identities which includes the identities of cis-woman and trans-woman. One can argue about the appropriateness of doing so all day, but it's not necessary to agree to the terminology change in order to accept what you say is step one.
Now, if I were to address the problem with logic, I'd say both sides attachment to the term "woman" are not strictly logical. They are just words, after all. But we are not talking logic. We are talking identity, emotion, and psychology. Not everything that is important makes objectively rational sense. And that's not easy for me to say because I generally tend to look first to logical arguments myself.
Not entirely related, but something to think on:
For some people, it looks like what is happening is this:
Trans activist: We are oppressed and want equal rights!
Feminists: We see you and support your struggle!
Trans activist: We should be treated the same as you!
Feminists: We can do that!
Trans activist: we want access to your spaces!
Feminists: Um, OK. As long as you meet X criteria and behave in manner Y.
Trans activist: We want full access! No restrictions.
Feminists: Now, wait a minute...
Trans activist: Full access! We are you! These are our spaces!
Feminists: Hold on now, these are women's spaces we have agreed to share with you...
Trans Activist: I am woman, hear me roar!
Feminists: Hey, that's our song!
(Felt a need for a Helen Reddy reference. Angie Baby was one of my favorite songs as a kid. RIP.)
Obviously, people with other viewpoints are going to see it differently. But that's the point. Instead of telling people they shouldn't see things differently, it is more productive to try and understand why they see it differently. And logic is the wrong tool for that.