"Parallel program"....excuse me if I am mistaken, but I thought we had already decided in this country that "separate but equal" is "inherently unequal". I believe that. I do not think you can successfully have a "parallel program". Which means they won't have any choice but to abandon the decision to admit girls or to fully integrate. And many units will go straight to full integration for the reasons set forth above...not enough volunteers, not enough resources, easier to plan program, etc. "Parallel program" is just proponents trying to have their cake and eat it too.
The BSA is not a public accommodation or branch of any government. So, like many others, it can offer separate programs by sex - as BSA has done for many years.