OK, so I think this conversation has got a lot more interesting compared to when it started.
The thread will be full up soon so I am going to add a final comment from me.
The OP was clearly not posting in good faith, claiming to be "in the middle". There has been a lot of discussion about whether there really is a middle ground and if so, where it is.
I think there is essentially no middle ground between "trans women are women" and "trans women are men". If you believe trans women are women you believe that what makes someone a woman is their gender identity and if you believe trans women are men you believe that what makes someone a woman is their biological sex. Nobody who is wedded to either of these positions is likely to be convinced to defect to the opposing camp.
From my point of view, I believe that trans women are men because for me the word "men" means "male people", and "male" is a biological sex, not a gender identity. I do not use the words "men" and "male" to hurt anyone's feelings; I see this as a simple statement of fact and I use these words for clarity. I lament the fact that so many really important words have been mangled and redefined in what seems to me to be a deliberate attempt to obfuscate the truth.
At the same time I can accept that using words such as "man" and "male" to refer to trans women may be hurtful. When the trans woman concerned is someone like Karen White or Isla Bryson, I couldn't care less about their feelings and will correctly sex them with impunity. Where the transwoman concerned is someone like @AlphaTransWoman, I feel a lot more uneasy about doing that. My intention is never to hurt people.
I find some of the objections to third spaces in this thread surprising and actually somewhat ideological. As gender critical feminists, we may prefer that everyone accepted their biological sex and used single sex facilities for their own sex without complaint. But that is not a realistic expectation. There are too many people out there who identify as transgender who consider this to be unacceptable, and they are not going anywhere.
In my view, the only way to get trans women to stop using women's single sex spaces, which I believe is what most of us here want, is to work with the members of the trans community who agree to work with us, and to say, "We hear you. You don't feel able to use single sex facilities for members of your birth sex. Many women don't feel able to use single sex facilities if transgender people who were born the opposite sex may be using them. Would you be OK with using additional gender neutral spaces if these were to be provided, so that the single sex spaces can be maintained as single sex? That way everyone is reasonably provided for and everybody has the opportunity to participate in society."
To me, that is the middle ground.
Opposing third spaces on the basis that you don't personally recognise the existence of a "third sex" or "people who are neither fully male nor female" strikes me as ideological. And that will never win people on the other side of the debate over. What is needed is a practical solution.
Earlier in the thread I linked to an article about Noah Ruiz, a trans man who was attacked in the US for using a women's toilet. Noah is female but presents as male. Noah's presence in women's toilets may legitimately be distressing for women, and yet Noah is clearly not safe in men's toilets. Since Noah apparently asked the owner of the park which toilets to use and was advised to use the women's toilets for his own safety, it seems likely that if a gender neutral toilet existed and he had been directed to use it, he would have done so.
So I can see the point of third spaces, and I think that this is where we are most likely to find some sort of middle ground.