GG could have avoided all of this with a bit of thought.
Either: they are single sex regardless of gender (presumably female)
Or they are single gender, regardless of sex (therefore mixed sex, like the scouts).
The first would welcome girls and transboys.
The second would require a change in their founding agreements and mixed sex safeguarding measures.
What they appear to be doing is confusing the two, causing a completely unnecessary fight. I am saddened as I loved being a guide, but until safeguarding is addressed, I am not letting DD do the same. At least scouts has thought about problems.