I am interested in understanding the role Christianity had in the development of the scientific worldview.
I know that the Church, as an institution, often clashed with philosophers and scientists that advanced ideas that contradicted the dogma.
What I would like to know is the effect Christianity - as a set of belief people had about the world and their place in it - had on the development of the scientific approach.
The Church clashed with philosophers and natural philosophers (the word 'scientist' was only coined in 1834 by - and this could sound ironic to people with a poor knowledge of history of science - a devout Anglican priest) that advanced ideas contrary to dogma only a very few times; not 'often'. The example that comes to mind to everyone is the Galileo affair (arguably the most misunderstood event in history): that's not a very good example, and this becomes clear when you seriously study it without prejudices. The so-called conflict thesis was born in the XIX century, after the publications of two infamous books by Andrew Dickson White and John William Draper; the Draper-White thesis is now rejected by virtually all historians of science, but is still popular between scientists and historically illiterate people. To address your question, I point out that according to the medieval doctrine of the two Books -the Book of Nature and the Book of God, ie the Bible-, that can be traced all the way back in the writings of theologians like Augustine, John Cassian, Chrysostom etc, but that was explicity stated by Konrad of Megenberg in his Buch der Natur (1349), not only could Nature be studied without any theological restraints, but should be studied, with the help of mathematics and the experimental method, because it was a way to render glory to the Lord and praise His Creation. Contrary to the popular opinion, a rigorous Biblical literalism was not the norm in the Middle Ages. Fathers of the Church like Origen and the already mentioned Augustine and John Chrysostom, didn't esitate in calling the strictest literalist 'idiots' and 'fools'. So Guillaume de Conches and Aquinas could expose proto-evolutionary theories without being burned at the stake; oddly enough, in the famous Condemnations of 1277, by Bishop Etienne Tempier (affecting only the theology faculty of the University of Paris), amongst the heretical propositions was the Aristotelian teaching that God had only created one world: that would clash with the omnipotence of God, so, ironically, it was not prohibited to talk about different, maybe infinite worlds, and extraterrestrial beings- not the opposite, as one would think. Literalism became a thing with the Reformation: so, in different Lutheran universities (not all of them), the teaching of Copernican theories was prohibited, while at the University of Salamanca, in obscurantist Spain, it wasn't, and the same in Italy (until 1616, of course). Now, about Christianity and the Scientific Revolution between 1543 and 1687 (before I talked about the Middle Ages, because the foundations of this Revolution were laid then). The first thing, the vast majority of the scientists in the Early Modern Period were really religious, and that can't be denied. Some could argue that X feigned to be religious because he was afraid of persecutions: but private diaries, documents not meant to be published, and other evidences prove that the majority of this majority was really devout beyond any doubt. But the important question is: Did Christianity have a positive or a negative effect on their researches? Did religiousity 'fuel' or hinder their activities? Well, for the XVII century, the former option is most likely the right one. Most scientist of the era thought that the scientific career was the best way to praise the Lord, and that the new discoveries provided the best proofs of God's existence : some remarkable examples are Antonie van Leeuvenhoek, Robert Boyle and Jan Swammerdam. People make always the same objection here: weren't the theological and biblical researches of a Newton a waste of time, that could be used better? Maybe they were; but maybe an atheist Newton would have been a normal guy, uninterested in studying the Creation, with an anonymous job, who spent his free time in worldly pleasures like taverns and harlots. Noone can prove that, as the 'waste of time' proponent can't prove their theory, or disprove the aforementioned one. So... To be fair, there are a few people that could have been 'stymied' by too much interested in religion: Swammerdam quit his scientific activity for 4 years, but then he went back to work; Niels Steensen (Nicolas Steno) put science aside after his conversion to Catholicism; Swedenborg had a crysis (kinda) and then he focused on some weird things, but let's say it just went crazy; Maria Gaetana Agnesi in her last years dedicated herself to charity and assistance to poors. But, really, I can't think of other people right now. On the other hand, I never hear people talking about the waste of time of ancient scientist with metaphysics or astrology or other hellenistic oddities. Nichomacus of Gerasa was a Neo-pithagorean interested with numerology and mistycs, Porphiry was pretty obsessed with horoscopic astrology, but okay... they were skeptical and rationalist atheists, as everyone 'knows'. So, the scientific Revolution didn't happen despite Christianity; but it either didn't happen thanks to Christianity 'per se'. The dogmas of the Trinity, the Virginity of Mary and everything else had no impact on science obviously. But the idea of a personal God, creator of the laws of nature, was instrumental in the revolution. And the supposed warfare between science and religion through history is 90% myth.
The must read on the subject are: -Edward Grant (God and Reason in the Middle Ages; The foundations of Modern Science in the Middle Ages; Planets, Stars and Orbs: the Medieval Cosmos 1200-1687; Science and Religion: from Aristotle to Copernicus);