I've written something about this, which will be relevant to things I say below:
Galileo and the Origin of Science
1) The article in question is almost entirely a summary of parts of a paper presented at a
department seminar, which I would say (given some familiarity with such papers) is part of an ongoing project by Benabou and coauthors that will probably end up in a peer-reviewed study in some form, but is in a far more "rough" form currently:
"Forbidden Fruits: The Political Economy of Science, Religion, and Growth"
2) The paper's models offer support for three models for the religiosity/scientific nexus: tendency towards theocracy and stifling the sciences, tendency towards secular worldviews and scientific development, and both. That is, they don't conclude that "science and religion are really enemies"
at all.
3) Both the seminar and study approached the issue not from a philosophy of science, history of science, or any similar approach typical for understanding/modelling the sciences, their nature, & their development.
4) The study didn't make use of typical economic research methods, although the approach taken is the only one that can be suitable for virtually all economic modelling. The problem is that while some in the social sciences have, for years, not only utilized a complex/dynamical systems approach but have contributed to our techniques for dealing with such systems, this study combines an incredibly simplistic dynamical systems approach with the usual reliance on unsound statistical procedures and statistical design (i.e., hypothesis testing or null hypothesis significance testing).
5) With the exception of a few studies, such as those (generally equally poor) by Stark, the authors don't deal with the literature on what the sciences are, how they developed, when & why the didn't, how they didn't develop in cultures in which concepts & technologies generally associated with the sciences did, etc.
6) The paper focuses the bulk of its historical summary on "the Church", but falls victim to common misconceptions such as Galileo and the RCC (for a volume with a paper in large agreement with this paper's conclusion yet with a devastating critique on the relevancy of the Galileo affair, see Numbers, R. L. (Ed.). (2009).
Galileo goes to jail and other myths about science and religion. Harvard University Press.). This has important consequences for the authors' later findings.
For example, in their analysis of scientific progress in history (which informs their current models), they fail to note what so confused Bertrand Russell: why a nation like China which had no religious obstacles to the development of the sciences and which, prior to the early modern period, was unsurpassed when it came to engineering and made huge strides in mathematics, still failed to develop natural philosophy- the
precursor to the sciences that began in ancient Greece and remained unsurpassed until development of the Western university system by the Roman Catholic Church as well as late Scholasticism.
The modern analogue would be the number of patents that is mentioned in both the article and the study as a measure of scientific progress/development. It confuses technological developments, which do not require the foundations needed for even the precursor of the sciences with the sciences. "Science"
requires a worldview in which it makes sense to investigate natural phenomena, understand these investigations in terms of order. Without a belief that the replication of a finding supports a general "law" there is no basis for empirical inquiry and no capacity for any empirical findings to connect with any explanatory theory/model).
7) For over a millennia, Christians and later Muslim scholars who drew extensively upon Aristotle failed to test his theory of mechanics (motion) which Aristotle could have disproved by one of many fairly simple experiments. It wasn't until Galileo that this was challenged and among the first empirical (scientific) studies conducted. And it was his challenge of this pre-Christian Greek pagan which was central to his trial and house arrest:
"It is true of course that in the seventeenth century the arch-Copernican Galileo Galilei (1564–1642) met opposition from Catholic authorities in Rome. However, their dispute focused on matters related to biblical interpretation, educational jurisdiction, and the threat Galileo represented to the entrenched 'scientific' authority of Aristotle, not on any supposed Copernican depreciation of the cosmic specialness or privilege of humankind. If anything, Galileo and his fellow Copernicans were raising the status of earth and its inhabitants within the universe."
Danielson, D.R. (2009). "That the Medieval Christian Church Suppressed the Growth of Science" in R. L. Numbers (Ed.). (2009).
Galileo goes to jail and other myths about science and religion. Harvard University Press.
8) In addition to a dynamical systems approach, the authors utilize game theory, a tool far more ubiquitous within economics. However, it is at best limited to the "game" specified in the mathematical models used in this or any other study as well as the mathematical "agents" in such models. The rather complete irrelevancy of agents which are necessarily defined by an economy that didn't exist long after natural philosophy had become "Science" render the model self-defeating. It attempts to demonstrate how the sciences do or don't progress given a socio-cultural context which didn't result in, or contribute to, the vast majority of developments required for the emergence of the sciences from natural philosophy as well, as the continued development of the sciences after the emergence of the scientific endeavor.
Basically, a failure to actually deal with what "science" is in order to build model(s) which demonstrate the factors contributing to its development, the use of overly-simplistic dynamical systems modelling and game theory, the reliance on an ubiquitous but unsound & empirically unsupported statistical designed, and the thoroughly economically-grounded approach to a field of inquiry that developed without the possibility of the assumptions made in the approach render pretty questionable the entirety of the study.
That said, the question is a broad one and the study wasn't your typical scientific paper. Further work distributed among several studies might prove very helpful, such as
1) those that deal with one of the three classes of models in-depth
2) one or more which deal with what "scientific progress" means
3) one or more which deal with what the sciences are and how socio-cultural norms, worldviews, etc., do or do not interact with the foundations of the sciences
&
4) those which don't rely on unsound statistics and incredibly simplistic nonlinear modelling but cutting-edge use of sound mathematical tools.