> the gap in science that emerged during the Counter-Reformation was enormous, lasted centuries

Was it now? I'd say France in the 1800s did a pretty good job about all the science stuff, and until Germany took the lead towards the end of that century (I'd say ~1880s) they were way above everyone else when it came to scientific discovery, way above the Brits, that's for sure.

If by "Catholic" the authors of the study basically mean Italy and Spain (which would be a very reductionist take, but suppose that they do that) then the decline in scientific thought starting with the 1600s has lots of other potential (mostly economics- and demographics-based) causes, not religion itself. Reminder that Giordano Bruno, who came from a Catholic country, had no opening at the very protestant Oxford, to quote wikipedia [1]:

> He also lectured at Oxford, and unsuccessfully sought a teaching position there. His views were controversial, notably with John Underhill, Rector of Lincoln College and subsequently bishop of Oxford, and George Abbot, who later became Archbishop of Canterbury. Abbot mocked Bruno for supporting "the opinion of Copernicus that the earth did go round, and the heavens did stand still; whereas in truth it was his own head which rather did run round, and his brains did not stand still",[33] and found Bruno had both plagiarized and misrepresented Ficino's work, leading Bruno to return to the continent.

Ah, I had also forgotten that Copernicus himself had been a Catholic canon.

So all this study is just, to put it plainly, absolute bs.

[1] https://en.wikipedia.org/wiki/Giordano_Bruno

Later edit: And talking about Catholic Spain, some of the most respected economists in the history of the dismal science were actually Catholic Scholastics, Schumpeter himself had almost only words of praise for the School of Salamanca guys that had written about economics, and in many cases he (Schumpeter) was trying to explain how the Spanish Scholastics had actually been ahead of their times in many domains of economics.