It's all about sex...
The crux of the article is thus:
"It took most of the 20th century for conservative women to adopt family-planning practices that have become dominant in American society," the writers said. "Or to put the matter differently, the so-called decline of the mainline may ultimately be attributable to its earlier approval of contraception."
With an interesting footnote:
However, the sociologists cautioned, it will be some time before the conservatives' "demographic momentum" exhausts itself -- perhaps 50 years -- because those born during the conservatives' belated baby boom of the 1970s will be filling those pews for quite a while.