For example, the British Boy Scouts organization is simply the "Scout Association" and has admitted girls under that name since the 1970s, though the British Girl Scouts organization is "Girlguiding" and is still for girls only.
Perhaps we Americans could rename the Boy Scouts and/or Girl Scouts to have a similar distinction as a way to smooth over this dispute.
(see https://en.wikipedia.org/wiki/Scouting and https://en.wikipedia.org/wiki/Girl_Guides )