Mumsnet isnt a great forum for debating people like Nicky as it's easy for posters to selectively attend (and ignore) points raised.
We all victims of confirmation bias, and I expect Nicky really did think she was answering all of the challenges posed and witnessing vile bigotry - based on selectively attending to specific aspects of posts. She clearly was feeling righteously indignant.
There is really no point of discussion beyond definitions if 2 debaters are using different definitions. The key issues are (I) does she accept or deny there is a fixed and immutable difference between natal males and females (ii) if she accepts these, her beliefs about where and when this difference matters can be discussed.
The challenge for Nicky, is that these two points can and should be debated without any reference to trans people. The starting point should be where single sex provision is deemed to be good (or acceptable). Then, a discussion can be had about whether those with a trans identity should or shouldn't be included - but only at this point.
Posters like Nicky, when starting at the point of 'trans inclusion', consider this to be the be all and end all. They can't see there being an issue outside of the trans inclusion aspect and I think they are so blinded by their passion for their cause that they really think the points we raise are driven by transphobia and a desire to exclude trans people - no by a desire for single sex spaces!