Recently, I read an article about how/why/when science and religion decided to divorce.
I think that the 'divorce' between science and religion was a slow and complex process in European thought. In order to understand it, it's necessary to look at the history of philosophy. A nutshell overview...
There have always been highly rational strands within Christian theology. It's never really been 'just trust the Bible' the way so many atheists want to portray it. If you study patristic theology in late antiquity, you see them using many of the ideas and much of the vocabulary of late antique Platonism (the dominant "pagan" philosophy of the time). The christological and trinitarian controversies are filled with it. Or on another more peculiar note, look at some of the things Augustine wrote.
In early medieval times, this philosophical theology declined along with the general decline in learning and literacy after the Roman empire collapsed but didn't dissappear entirely. We still see it in writers like Eriugena and many of the Byzantines. It was strongest in the east where the earliest Muslims inherited it, leading to their short-lived intellectual leadership during their golden years as they took the inherited Greek ideas in new directions.
Then in the high medieval period we see the rise of the medieval universities, and along with it some very sophisticated work in logic (that's still underappreciated today). There was an interest in physical problems as well, especially in England it seems, with productive work in areas like geometrical optics. We start seeing eyeglasses coming into use in this period. In Germany it was clockmakers, and lots of experience was gained in geared mechanisms.
And it was a period noted for the struggles for and against Aristotle, whose works had been recently rediscovered (from the Arabs and Byzantines). At first the church tried to outlaw Aristotle, which naturally turned his writings into an underground sensation in all of the hippest 12th century Paris cafes. All the intellectuals were reading Aristotle, even on pain of ex-communication. So Thomas Aquinas produced a definitive synthesis of Christianity and Aristotle, that later became the official philosophy of the Roman Catholic church.
Once Aristotle became the philosopher officially taught in all the universities, intellectuals started seeing him as a cold dead hand suppressing free thought. (We still see a bit of that kind of hostility to Aristotle in some writings today.) But this little history has arrived in the Renaissance, when recovering ancient classical texts became Europe's(or at least Italy's) fascination. Pretty much all of the surviving ancient Greek and Roman texts that we have today were recovered by this time. They included all kinds of things, most notably the more mystical Neoplatonists and the Skeptics, who set European intellectuals on their ear.
Most of European thought from the Renaissance to now has been a giant reaction to the Skeptics.
At first, religious thinkers typically embraced the skeptics, arguing that if the skeptics were right that no knowledge can have secure foundations, then we should go with the ideas that have the strongest basis in tradition and everyday life, namely the deeply entrenched religious beliefs and the traditional teachings of the church.
Then along came the 16th century and the protestant reformation. The reformers turned the new skepticism on Mary and the saints, on miracles and on all of the familiar side of catholic popular religiosity. All in favor of a "reformed" Bible-only,
"sola-scriptura" religiosity. In a way, the protestants were the anti-"woo" skeptics of their day, laughing at all the village Catholics who believed that praying to saints or to Mary could bring about miracles. Superstition! The medieval monasteries were torn down and all of the monks practicing their contemplative disciplines dispersed. Religious art was condemned and a new austere aesthetic appeared of bare churches and black and white.
Of course it only took a few years for European intellectuals to turn that same skepticism towards the protestants' sacred Bible, and in the 17th century we arrive at Deism, a generalized skepticism about any form of revealed religion. The only credible basis for religious belief as they saw it was Natural Theology, the ancient (they pre-date Christianity) first-cause and design arguments, and all of their cousins. That was the strand of thinking that was later to loosen the grip of Christianity on western thought and turned into full-frontal atheism in the 18th and 19th centuries as natural theology was abandoned, capped off by Darwin and the damage that many thought that he had done to the design argument.
But the protestant reformation wasn't the only effect of the new skepticism on European thought. Many thinkers started thinking that if all of the old authorities don't suffice to support the intellectual edifice, new foundations must be found. In many cases, that strand of thinking was essentially a search for some alternative to Aristotle (who was still taught in the universities). So we see things like Descartes'
Meditations, rhetorically accepting the skeptics' arguments that pretty much anything can be doubted, and searching for something... anything... that seemed indubitable. Descartes found his 'cogito' (I think, therefore I am) and ultimately tried to use it to justify his faith in mathematics (he was a mathematician) through 'clear and distinct ideas' (an idea that Descartes had lifted from the ancient stoics whose writing had been recovered in the Renaissance). So modern philosophy was off and running.
Meanwhile, around the same time, people like Galileo, Kepler, Descartes and ultimately Newton were responding to the universal skepticism by searching for new and more secure methods and foundations in natural philosophy to replace Aristotle's physics. They began applying mathematics to a class of simple physical problems, motion down inclined planes, falling objects, pendulums, and (strangely enough) the motions of the planets in the sky. And sure enough, they found regularities that they could describe and model with the mathematics that they had available. (Or they could expand that mathematics in interesting ways, as Newton and Leibniz did with their new calculus.) That news created an intellectual sensation in the early 18th century when Newton was elevated into a demi-god, the "Einstein" of his day.
So in the Enlightenment, everyone wanted to figure out what
wonderful new method had been discovered that enabled such impressive achievements in natural philosophy. How had skepticism been defeated? (If only seemingly...) By the time of the French revolution we see reformers insisting that if the new methods could only be applied to society, then all sorts of obscurantism could be swept away, truth revealed and a secular paradise constructed. We are only slowly moving away from that idea today, since (as always) it isn't really clear what will replace it. It's the faith that I still sense motivates some of the participants right here on Sciforums. It's what lies behind your original question in the OP.