As a legal matter, you start getting into a grey area. Does the PTO receive any public support? The reason that Exploring was moved from the Boy Scouts of America into an affiliated corporation, Learning for Life, was because Law Enforcement Career Exploring Posts and Fire & Emergency Services Career Exploring Posts were often sponsored by Police Department or Fire Departments.
The ACLU was successful in winning suits against the Departments and the BSA because of the mix of public funds and the BSA's policy that youth believe in a higher being (God - as you define him or her).
Exploring was moved into Learning for Life, which doesn't require belief in a God, and Venturing was eventually introduced into the BSA as the co-ed program for the BSA.
The Boy Scouts have female leaders at all levels (I know plenty of female Assistant Scoutmasters and a few female Scoutmasters, and the world is chock full of female Den Leaders, Webelos Leaders, and Cubmasters). They camp with their units.
If you're male - say, a divorced or widowed dad - and you want to be active in Girl Scouting with your daughter(s)? Good luck. They few I know who manage to fight the battle face discrimination. At summer camp, they are either herded into a building and locked in at night, or they are transported in vans in the evening to another site.
Why? Well, because you have to protect the girls from possible sexual abuse.
It doesn't matter than the Girl Scouts have openly lesbian leaders, or that there seems to be some strange hypocrisy to the idea that girls must be protected from men, but boys don't require protection from homosexual men.
The Girl Scouts are immune from criticism.