1940s
This was true in my own experience:
I was in the Boy Scouts in the 1990s. I witnessed my own troop’s decline as an institution. The troop actually folded, for lack of members, in the mid or late 2000s. The reasons were various. The biggest reason, or so was my conclusion at the time, can be seen in the thousand-words spoken by the paintbrush of Norman Rockwell, over there —->
The typical kid born into the 2000s-USA will not identify with that image. It is an “America” that Whites associate with the 1950s. That was (and I guess still is) its appeal.
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I tried to find numbers. The best I can come up with:
2.7 million : 2011’s tally for number of boys in the Boy Scouts. [Official, pdf]
3.5 million : The 1990s tally, when I was involved. [Apparently official / excluding “Learning for Life” members]