The Boy Scouts in its first iteration was a non-sectarian Christian Organization at large.
In its local organization it could be Baptist, Catholic, Methodist or Anglican. Basically it could be organized around a particular local Christian church.
Once the Scouts started accepting homosexuals many Christian church abandoned the Scouts and start organizations like the Navigators. (https://www.navigatorsusa.org/)
I am not advocating the Navigators. It is just the alternative that came to mind. The Masons do not and did not care what deity or deities you worship. They care only that you acknowledge a superior power.
You’re correct. A better comparison than the Boy Scouts would be Alcoholics Anonymous.