Morphine thanks for replying. I will just answer and then I must go to bed so I am not ignoring you but the divan is calling!
girls are not 50% of the population and Girl Guides is for girls aged about (I can't remember) 10-18. So not 50% of even the female population.
And women and girls only need safe spaces because they are being marginalized.
I don't understand your use of 'femininity' here. My daughter is not very feminine at all. She hates skirts, loves trousers and used to be magnificent at climbing trees. I don't send her to Guides to become 'feminine'.
'Safe' doesn't just mean from physical attack. It might be a safe space to explore what being a girl is all about. Just as a trans person may wish to talk about issues specific to being trans in a specific club or activity for trans people.
Plus one very important thing that is lost if you allow any males into a club for females, is the idea of being allowed (by males) to have a club just for females. Just think about that, who is allowing or not allowing us to have a club for only girls, males. That bit of the club has now been controlled by someone else. Partly it is the principle that 'we' or rather 'they' (girls) do not get to decide.
Girls are a lot safe in female only spaces than they are elsewhere. But, I don't want to stop my daughter from mixing with boys. She goes to a mixed/co-ed school, she goes to activities where girls and boys will be present. She has a brother and father, and me!
The only activity in her life that is female only is Girl Guides. Who has the right to take that away? When there is a scouts group in our area which, I believe, takes boys and girls.
You said "The space is a female space...free from what? Domineering boys? Over competitiveness?"
The space is a female space...free from .... males.
Yes, some boys are domineering. The teachers at school certainly spend a lot more time dealing with noise and issues from the boys, so it seems. But even if the boys were as quiet as mice, it doesn't make them girls, or indeed mice! 
Why would make you think I want to keep my daughter away from over-competitiveness? Or that being in only female company would ensure that? Girls can be very competitive.
In my area the only other thing that springs to mind is female only swim sessions at the local pool. Is that OK? Or should males be allowed in there too?
"gender segregation" You use the word 'gender' a fair bit. It doesn't really mean that much to me. Some limited sex segregation seems fair enough in a wide variety of situations.
And where women do not want to be segregated by sex there are usually other options - mixed sex schools, mixed sex clubs, toilets that are unisex rooms on their own, general pool times when anyone uses the pool etc.
So women and girls can always choose not to be sex-segregated if they wish to be.
But this argument is clearly not about what women and girls want at all.
For the record I would have huge sympathy for a trans girl wanting to join in activities with girls, but it is not for me to say what other girls will want to do, or what other parents will be happy with. A trans girls would be welcome to a whole bunch of things if I was organizing them. But telling all girls they cannot expect a single-sex environment for any group activities....That's not my place.
Just imagine if girls were trying to shut down trans only spaces. But as far as I know, they are not.
Night Night (again!)