There are three key paragraphs in the quoted article worth paying attention to:
Working under the assumption that more time spent under church rule would ingrain those values more deeply, the researchers compared psychological and kinship traits of modern populations with the time their ancestors spent under Roman Catholic rule. The researchers built a vast database from historical records of church exposure in every nation on Earth, beginning in the first century and ending in 1500 C.E., when European society had become nearly fully Christianized.
Next, they consulted anthropological data to assign a kinship intensity score to each of the world’s major ethnolinguistic groups. This score was based on historical rates of cousin marriage, polygamy, and other factors. Finally, they drew on dozens of studies that used established psychological measures such as the World Values Survey to determine modern population-level scores for traits such as individualism, creativity, nonconformity, obedience, and ingroup/outgroup trust. (Two of the more unorthodox measures of obedience and outgroup trust, for example, were unpaid parking tickets issued to United Nations diplomats and participation in blood donation drives.)
Plotting these points together, they found that the longer a population spent under the rule of the Roman Catholic Church, the lower its kinship intensity score, meaning lower rates of cousin marriage and polygamy and looser familial and clan structures. And as kinship intensity drops off in their data, a certain suite of traits grows stronger, including individualism, nonconformity, and willingness to trust and help strangers, the researchers report today in Science.
Before we dismiss this entirely merely because of the subject matter it treats, the methodology looks sound — it reads to me like they've just built a multi-variate model and looked for correlations. Because they do appear to have temporal data on more than one variable, it's easier to push correlation into causal relationships.
Where I would question the soundness of the research is on the quality of the data. They would have been working with historical data from mixed sources, which would have a high amount of variability — it would have been noisy and uneven. It'd be good to have an understanding of how they went about normalising the data that fed the model, to arrive at their conclusions.