Admirable though it is for people to get involved in arbitration and negotiation between two dissenting factions, for me, in this particular issue, it does not apply.
I don't view this as a clash of rights between two equally valid opponents. It's about the domination of one group over another. Which, by its very nature, involves removing things from that second group which are necessary for their equality.
Personally, I disagree with the very concept of a 'solution'.
The men who want to use women's spaces are using the women in them. It's not the space, it's the women in them that validate their 'gender identity'.
If all the women moved to a different space, the focus would be transferred from the first space to the second space. The first space would be entirely unappealing. It's the presence of the women and girls in it, that is the crucial part.
Whether that space is a prison, or rape refuge, a ward, an online dating service for lesbians, sport or the very concept of what it means to be a woman.
This need for validation is, for many men, a paraphilia. And even those for whom it isn't, using women in this way still a boundary violation. And displays a sense of entitlement that means they can use the presence of women and girls in their own spaces, set up to address sexism, for their own ends. It's sexism on steroids.
So I'm not happy even being asked to consider the concept of solving that problem for these men.
The very most I will offer, is telling them to keep out of women's spaces. And I will simultaneously campaign to expose the sexism underlining the ideology.
My 'solution' is to dismantle the ideology. Not provide a means to make it more acceptable, or accommodate it.
This isn't an 'issue' for women to solve. It's a wholesale attack on their rights. And because we have fought tooth and nail to protect our rights, and have had a modicum of success in certain areas, we are expected to 'compromise' over others.
In order to be 'fair'.