I think the concerns extend beyond periods and sex. I think the concern I have would be turning Boy Scouts into a watered down camping club for the older youth and a glorified day care for the grade schoolers. I don't believe adding girls would have to result in those changes but it is a risk based upon some of the language being used. I think it also depends on which girls join Boy Scouts. If the tomboys, for lack of a better term, join I don't see an issue. If girls join and push scouting to more about STEM and other non outdoor activities ... it could permanently damage Boy Scouts.
If Boy Scouts keep their patrol method and continue to be an outdoor driven program with minimal changes, I would welcome adding girl members. We had a few girls go with us on a 100 mile canoe trip in the BWCA with no issues.... they were considered one of the guys. However, I could also see this go south fast.