I’m not sure of SP’s exact position on this, but from the earlier parts of the discussion, it sounds like her specific objection is to self-ID.
I think she might be one of the more middle-of-the-road campaigners who still feel concessions to transsexuals might be reasonable.
Of course the wheels always come off that one because as soon as you admit any man, you run into the problem that it’s “not good practice” to demand other men medically modify themselves to achieve the same rights. So the admission of any medically transitioned man, immediately results in any non-medically transitioned man having the same rights.
Lots of us started out objecting to self-ID but have gradually concluded the only way to protect women’s rights is to remove the GRA as it is fatally flawed because of that. There are still a lot of people arguing that middle ground though, to the point where there’s a significant split in our ranks at the moment.
Still, suffragists and suffragettes both existed and argued, but women still got the right to vote.