I think you are once again hitting that logic trap. Because there was a drop in the rate of Christians in Europe during these bad times does not automatically make that the culprit, if a culprit exists. There are those who believe that the stable population rates in Europe are the best thing that could happen while Europe sorts out its priorities. Clearly the two specific reasons for the population growth rate reduction are birth control and emigration. Not sure though how that compares to the Black Death.
The author's view that among other things, the culture going defunct is resulting in civilizational suicide is not supported by the facts. Almost every nation in Europe has a higher literacy rate than the US. Whether we approve or not, crime rates are generally lower, and health is generally higher. I'm not aware of any of those countries that are not democratic, so apparently the people are satisfied with the progress.
Europe is a net importer of oil and does have environmental problems, so perhaps a stable or lowered population growth is a good thing, at least from that viewpoint.
It seems clear that the two wars and two tyrannies which left Europe devastated were the principal causes of its current policies toward centralization for security, to restore the environment, ensure economic stability, high education levels, and a healthy and prosperous population. If those goals are destroying a culture that permeated Europe in earlier periods, I see no Europeans shedding many tears. Nor do I hear any of them describing all of this as civilizational suicide. It may turn out that way, because most flirtations with centralized government and socialized economies have failed in the long run. But to believe today's Europe fails when compared to the historical Europe is simply to deny reality.
Indeed time coincidence is not proof. The proof is in the article -- at least in shorthand, and if certain code words such as "culture of death" are not meaningful to a non-Catholic, I can explain.
The literacy rates and such are surface. The overall contentment is in itself a bad symptom. What we have is the two wars, the two totalitarian plagues and voluntary depopulation (it is not population stability -- the numbers, and the comparison to the Black Death are in the article), accompanied by Islamization. Call it what you will, it is unprecedented and requires explanation. You did not offer any.