Religion and Science were never opposed
The following is adapted from a comment I left on a facebook post which argued that religion has played a significant role in retarding innovation and scientific progress. This is by no means meant as an attack on the person who posted it; they are in fact extremely well-read about many things, which is why I was so surprised to see the old myth of "religion vs. progress" revivified in this context. It comes off the back of a particularly frustrating evening spent defending the idea that science is not, in fact, a transhistorical arbiter of objective truth (shocker, I know). A more full-blooded defence of the discipline of philosophy of science will have to wait for another time. Instead, here's a brief exegesis of the history of science and religion. Please forgive the slapdash nature of some of the argumentation and references. I mostly wanted a go-to for when this argument comes up again.
Science and innovation were far from dead in the "Dark" or Middle Ages.
A lot of that rhetoric is strongly influenced by hindsight bias, particularly towards the Romans (who, by the way, also had religion - it just can't be the case that religion is intrinsically antithetical to scientific and innovative endeavours if some religious societies managed to innovate whilst others didn't). Here's a reasonably good source on this: https://explorable.com/middle-ages-science
It's worth noting that religion and science (and particularly Abrahamic religion and science, which are subject to the most egregious myths and distortions) just *weren't* opposed to one another. Classic examples of this:
1. Isaac Newton is seen as one of the greatest scientists of all time. Did you know that he spent a significant amount of his life exploring alchemy and Christianity, particularly the Apocalypse? (https://en.wikipedia.org/.../Isaac_Newton%27s_occult_studies is very well referenced). Even the idea that light has seven colours (cooked up by Newton) is plausibly influenced by Christianity: who the fuck genuinely thinks that violet and indigo are *actually* different? Seven has a significance in theology that six just doesn't. (Though this is disputed by some scholars who argue that he split light into seven colours in order to develop an analogy with the musical scale http://onlinelibrary.wiley.com/.../col.5080100411/abstract).
The point here is that the religious and scientific endeavours of a man who was undoubtedly a great scientist are *completely inseparable*. You can't have Newton-the-inventor-of-calculus without Newton-the-student-of-the-apocrypha.
2. Robert Boyle (of Boyle's law and air pump fame) "viewed his theological interests and his work in natural philosophy as forming a seamless whole and constantly used results from the one area to enlighten matters in the other" (https://plato.stanford.edu/entries/boyle/). His Christianity is inseparable from his science.
3. The idea that human cadaveric dissection was prohibited by the Catholic Church is a 19th century myth. In fact, in Middle Ages Rome dissection was done almost exclusively under the auspices of the Catholic Church (I don't have a source from this, but it comes from a lecture given by Simon Schaffer, an extremely well-regarded historian of science). The Catholic Church never took (and indeed does not take) a position on human dissection (http://web.b.ebscohost.com.ezproxy.is.ed.ac.uk/.../pdfvie...). Indeed, the interest in dissection of women specifically was rooted in a desire to understand the origins of human life, and so was sanctioned by the Church (https://news.harvard.edu/.../story/2011/04/debunking-a-myth/). It's a myth that just will not die.
4. The very term "scientist" was coined by a devout cleric, William Whewell (also one of the forefathers of modern philosophy of science). His entire justification for the idea that science can tell us *anything* about the world is theological: "On Whewell’s view, we are able to have knowledge of the world because the Fundamental Ideas which are used to organize our sciences resemble the ideas used by God in his creation of the physical world" (https://plato.stanford.edu/entries/whewell/).
5. The current conception of science and religion as fundamentally opposed comes in no small part from the efforts of John William Draper and Andrew Dickson White, who propounded the conflict thesis (https://en.wikipedia.org/wiki/Conflict_thesis) in part through misrepresenting the famous confrontation between TH Huxley, "Darwin's Bulldog", and Bishop Wilberforce, over the theory of evolution by natural selection. White, for example, published " 'A History of the Warfare of Science with Theology in Christendom', the culmination of over thirty years of research and publication on the subject, criticizing what he saw as restrictive, dogmatic forms of Christianity" (ibid.). Essentially, it's ahistorical at best and anti-historical at worst.
It's worth noting first that much of the reason for the controversy caused by Darwin's The Origin of Species when it was published was because scientists had been so attached to scientific theories with a theological and metaphysical basis pre-1860 (http://www.blc.arizona.edu/.../Giles%20-%20Huxley%20..., p291). The idea that evolution itself is fundamentally anti-religious (and so ought to be condemned by the Church) is also untrue. It was precisely the *non-progressive* conception of evolution that caused an issue; Darwin was far from the first evolutionist (his relative Erasmus Darwin was one, for a start) but he was one of the first (hat tip to Alfred Wallace here) to propose that humans were not the pinnacle of evolution, and that evolution was intrinsically adirectional (and even that's an oversimplification). Many Christians were also evolutionists (indeed, many are today - and some of them are progressive evolutionists in the vein of their forbears).
6. More generally, you might look at blog posts like this and the books linked in them, which detail the myth of the conflict between religion and science at some length: https://scienceandbelief.org/.../the-christian-roots.../...
That's probably enough examples, but the overall thrust is this: to talk of science and religion as two separate phenomena is nonsensical pre-19th century, and much of the opposition created between them comes from politically motivated writing and revisionist history from the conflict over the theory of natural selection in the late 19th century.
To argue that science and religion are opposed, or even that religion has played a major role in slowing or stifling innovation in any period before the late 19th century, is an intellectual position that is difficult to maintain with a modicum of knowledge of the history of science and medicine.