Historians have asked if the US was qualitatively different from other countries. ("Vineyard of liberty" etc.) The issues raised by the book give us another way to address the question. Perhaps Americans were more inclined to join such nation spanning groups because as an immigrant, footloose people, if they did not have centuries of binding to the same soil and neighbours, they wanted some other and multiple means of belonging? Was the striking success of the groups in some part due to such inchoate urgings?
Another way to test would be to look into the history of similar groups in Canada, Australia and New Zealand.
Skocpol also points out that from the 1960s onwards, the membership of such groups in the US fell significantly. She advanced several reasons. But there is one possible reason for some of the decline that she did not mention. From the mid 1950s, TV became pervasive. Remember that joining a volunteer group is done in your recreational time. TV is a notorious competitor for that time, due to its convenience and cheapness. Plus, and more specifically, if one of your reasons (possibly unconscious) for joining a national group is to be part of a larger world, then TV assuages that to some extent. Granted, some of this may be illusory, but so what?
Diminished Democracy: From Membership to Management in American Civic Life is Volume 8 in the Julian J. Rothbaum Distinguished Lecture Series.