I recall seeing some reporting on research about this. The problem that I had with that study, is that it seemed to be working from the assumption that decision of whether or not to cohabitate before marriage was akin to a coin flip for the population. The study controlled for a couple factors like education and claimed religious and political affiliation, but I contend that these controls are insufficiently granular to capture potential fundamental worldview differences[1]. Therefore, I contend that the conclusion that the decision of whether or not to cohabitate is the primary causal factor (rather than merely an indicator of an unidentified effect) is invalid because the two groups are unlikely to be sufficiently similar for outcomes to be assumed to be directly transferrable.
[1] For instance, there are portions of the republican party that would not condone the decision of a couple to live together before marrying (e.g. many of the religious conservatives), but others that would be expected to tend to be indifferent (e.g. much of the business and libertarian contingent). The same logic extends to claimed religious affiliation. For instance, I think that the Catholic Church's official stance would be against cohabitation before marriage, but among people who identify as Catholic, there are varying degrees to which the certain official policies are considered practical and/or legitimate. Keep in mind, lapsed Catholics/Jews/Muslims/Protestants/etc that still identify culturally with a religious group are counted as among those groups under the methodology. Overall, I would have felt more comfortable with the legitimacy of the conclusion if instead of looking for rough indicators of attitudes toward pre-marital cohabitation, they would have just chosen a few cohorts, and directly asked what their attitudes toward pre-marital cohabitation were, and then controlled for that factor.