I agree that 'sex segregation' has negative connotations of women being hidden away or pushed to the back.
I do like DonkeySkin's suggestions of single-sex services and spaces and single-sex provision, which I think is clearer than just 'single-sex' on its own.
Several posters have raised the issue of things like hairdressers and book clubs being included alongside changing rooms and refuges. How about separating what most people would see as essential single-sex services which should be kept, rather than simply an option, by rewording the heading on page 3 to:
When is the retention of single-sex services important?.
You could then keep section 1 (sport) and section 2 (facilities, services, accommodation) under this heading, but split section 2 into 2 parts by adding the paragraph about refuges and Rape Crisis (which you have currently put as section 3, part 1).
You could then have another heading:
When is the option of single-sex services important?
and possibly re-jig the remaining points so that the current section 4 (learning, education and development) comes first, with the remainder of section 3 last (simply because I think the general public will find education more important than book clubs or beauticians).
This means that the last sentence of page 2 would probably have to be reworded too, perhaps to something like:
This campaign is for the right to choose and access single-sex services and facilities where needed. People who do not require these single-sex services can therefore choose not to use them.