Science, as it is practiced in our western civilization, is a creation of the Church. Who else had the time, resources and people to form an international network where one could spend a lifetime studying nature and exchange information, along with an infrastructure that included libraries and copyists to ensure that copies of books were available to others around the world (at least, in the Christian world). This is how universities came about.
For example, the very basic principle we still use to make theories better, comes from a Franciscan Friar who made it popular in the 14th century.
The problems come when some religious groups don't like the results from science because the results contradict some lies that they were perpetuating. The Catholic Church lived through that in the 16th and 17th centuries.
Now they know better.
Many scientists are still very religious people, some being members of the Church.
Father William of Ockham is the 14th century friar who popularized the Law of Parcimony (today, we call this principle "Occam's Razor").
Pierre-Simon Laplace was studying in theology when the priests responsible for the school determined that he would be far more useful for society if he continued studies in science and mathematics. He came up with a theory on the formation of planets from a nebula (1796). The Catholic Church was happy because, so far, the only other logical approach for such a theory had been formulated by Emanuel Swedenborg who was also a theologian... but not a catholic one (an example of the far-more-common conflict between religion and... religion).
Unfortunately (for science), Emmanuel continued his work in theology, explaining such things as the nature of the Holy Trinity. I say "unfortunately" because of the 62 year gap in research between Swedenborg's idea and its pursuit by Laplace. I also say unfortunately because Emmanuel ended up concluding that the Last Judgment has already occurred (in 1757).
Charles Darwin was raised both as a Unitarian and an Anglican, giving him access to the best schools in the area. He was neglecting his studies in medicine, in order to further his studies to become a parson. His teachers and his parents worked behind the scenes to re-orient his studies so that he could complete his Medical degree.
Of course, Evolution was already accepted as a fact by the Church. What Darwin did is propose an idea to explain how it worked (Natural Selection). The idea that evolution could work without divine intervention, that is the part that shocked a lot of people at the time... including Darwin himself (he begged scientists to prove his theory wrong -- they tried).
Father Lemaitre was already a priest when he came up with the Primeval Atom Hypothesis (which became what we call the Big Bang theory). He never suffered any doubt to his faith. Even the Church found no problem with his idea, as they made him a Honorary Prelate (rank equivalent to bishop) for his work in science.
As a matter of fact, the "Big Bang" is an awful name for the theory because it causes confusion. The name was given by a famous astrophysicist (who also happened to be a proud atheist), during a radio interview. Unfortunately, the name stuck. This was a different example of a science versus religion conflict (this one showing that atheism is, itself, a form of belief). Fred could not stand the idea that a priest came up with a theory that allowed the universe could have a Creator.
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There are presently some problems in a few English-speaking countries, where groups of pseudo-Christians are trying to push their own interpretation of the Bible, and where this interpretation clearly goes against even the most basic observations. This is not a religion versus science conflict.
This is a political conflict (they want to get control of the education system so that their lies can be taught as if they were as true as scientific evidence).
Science and religion can and must co-exist. In fact, they created each other. They can even be seen as two separate eyes, looking at the same thing (God's creation).