conclusions of the researchers, to the extent they match the article, are over-reaching. All the study does is tell you which states give you the best government benefits for families with two working parents. No more. No less.
Schools benefit from having stay-at-home moms. When I lived in Las Vegas, a non-member school teacher told me many teachers in Clark County try to get jobs at schools with high LDS populations because the parents have greater ability to volunteer and they are more on top of what's going on in the school. With more volunteers, kids get more individual attention. That would seem to be a "family friendly" feature that isn't even remotely addressed by the study. Same with rates of crime, violence, graduation, two-parent families etc.