Think you are over analysingNo.
It's possible to believe that transgender identity is real, valid, and important, but that it is not the same identity as women.
For starters, no one is saying that transwomen are the same as cis-women. But what perspective one terms "cis-women" perspective 2 terms "women." Therefore the statement in the language of perspective one that:
"Trans-women and cis-women are different."
Can be translated into the language of perspective two as:
"Trans-women and women are different."
Those two statements say the same thing, just in different languages...or rather vocabularies.
So it is possible to believe that trans-women are not women (by the speaker's definition of woman) and yet fully support transgender rights.
You can also say "trans-women are not women" and also say "trans-women are not men, either."
How? Even if sex is binary, there's no reason that gender need be. And I'm not talking about things like autismgender (https://gender.wikia.org/wiki/Neurogender )
One could consider trans-woman (or trans-man) to be an identity/gender in and of itself that doesn't need to be the same as "woman" to be valid. In the end you still have to decide which facilities are segregated, whether they are segregated by sex/gender, and (for those segregated by gender) which gender uses which facility. But all genders would still be equally real and valid.
Frankly, I think the "Are trans-women women" argument gets in the way of a lot of practical common ground as well as resolution of trickier issues. For some women, and I'm guessing those who have devoted a significant part of themselves into feminist causes (yes, radical feminists...not meant as an insult) claiming what they regard as their identity for someone else probably feels like an attack. It puts them on the defensive and results in needless antagonism.
Basically to me at least.
Trans women aren't "females"
But I am OK with it if the want to be treated as "women", within reason.