Finally printed it out and am reading it more closely. There seems to me something she is not examing: It may not be that smaller families cause a decling in religion but that whatever causes smaller families also causes decline in religion.
From what I've observed in religious people, such people are much less inclined to 'play God' (whatever that means). This means they are less likely to take deliberate effort to direct their lives and limit the number of children. Non-religious people are more Promethean and willing to take deliberate action to create their lives. So, what may be happening is that a certain kind of personality is evolving in the modern world (the Promethean person or in economic terms, the capitalist rational man, or the Nietzschean proto-Supermen) which in the short term to individuals means they plan their families, and in the long term, find religion less relevant to their lives.

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1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13