As someone mentioned above when it first started as a grass roots based archive it was very much WLM politics.
In fact one of the lesbian archives in england sent all their papers to them believing they were a better (politcally) organisation than the feminist archives that had all disappeared into mainstream libraries.
But this is what happens when you need lots of money to keep a building going. The Feminist Library in London now has shiny new premises and trans inclusive politics.
The Women's Library Glasgow are clearly saying we dont like your politics so you cant speak here. So it may depend on whether any of their funding streams have conditions about free / open speech.
But as we know the establishment in Scotland has been captured by the trans narrative and it is now accepted practice in universities, and libraries to categorise GC discussion as hate speech.
It looks like that yet again unless there is somehow a court case that says they are wrong, this will just be another example of how well planned long term strategies by trans activists going back over decades are bearing fruit for them - and nothing for women. 