I am coming from another culture, so would some kind soul explain to me how, in the 21st century, the society tolerates an organization called "Girl Scouts"? Am I the only one seeing something wrong there, as if there would exist "White Scouts", for example?
So the reason of having segregated scouts is to protect their privacy? Wouldn't it be enough just to have one scout organization and separate bathrooms as well?
Privacy in bathrooms is accommodated through the use of private stalls. Why should you have privacy from someone with different body parts but not privacy from someone with the same body parts? What about transgendered people, or people born with a mixed gender? We all make the same body noises so if the privacy is there via private bathroom stalls, why segregate people?
Regardless of that point, the question was why "Girl Scouts" but not "White Scouts". Modern society frowns upon segregated bathrooms by skin color (look to the southern US for relatively recent examples of that) but not based upon sex. So just as there are segregated bathrooms for male vs female, there are also segregated baseball and volleyball teams, segregated schools, and many other examples where the division is by sex.
Maybe Scouts is one example where it should get with the times and there isn't a particularly good reason why it should be divided by sex, as could be argued for some sports where there are physiological differences justifying the segregation. However, I don't find it particularly archaic that a private organization exists which has separate groups for male vs. female. It would be archaic if only the female group has sewing, or only the male group has hunting, and if that is the case they should modernize those areas.
But it is a private organization and if people don't like the way the organization is run they are free to not participate. Anyone can start up their own private organization which allows members of either sex. Call it the Adventurers or the Pioneers, and have similar achievement badges. That sounds like a good idea to me.
I'm not sure how things are in the US, but I do know that in the UK we have the Boy Scouts and the Girl Guides, and they both allow members of both sexes. But you do tend to get a lot more girl scouts than you do boy guides.
Here in Portugal we just have the Scouts, and they're unisex. Well, actually we have two Scout groups, the Catholic and the secular, but they're both unisex.