Science in it's current form has not existed in the same way as today. I have always learned from popular culture and some documentaries that Christianity has always had a certain anti-science stance, but most of the supporting evidence doesn't hold when I learn more about those themes. Most of the time it seems to compare current empiricism with old times politics and truth searching disagreements that don't really compare. For some examples, please correct me if I'm wrong in any of those:
Galileo was working for the catholic church and his problems were mostly from politics with scientific rivals and writing a book insulting the Pope when he was asked to write a book comparing the heliocentric and geocentric models. He could also not prove the complete heliocentric model, just that Venus orbited the Sun, not the rest of the planets.
The dark ages is a concept completely disregarded by historians.
The supposed burning of the library of Alexandria by Christians wasn't burned by Christians and while it was an awful lost of books it wasn't a big loss of scientific knowledge.
Charles Darwin was buried with honors by the church of England.
The inquisition was more about prosecuting false converts than anything else.
So those are usually the big examples of the church being anti-science that don't seem to hold. Most of those examples seem to be people having problems with their time's believes and politics more than any church actively pushing against them. So the church may have been anti-science, but which would be the real examples for that or on which points am I wrong.
I understand that currently there are some problems with certain brands of Christianity with a clear anti-science stance, but has that been true historically?
We do have a (fairly large) section on Christianity and Science in the FAQ if you haven't discovered that yet.
It might help to clarify whether you're referring to Christianity or The Church - both are somewhat vague terms after the Reformation. Until then, we have the Catholic Church, which supported all manner of scientific endeavors. After that, everything splinters into numerous groups, some are more anti-science than others.
It also might be worth considering what you mean by 'anti-science'. Most Christians were not against science per se - what they objected to was the removal of God from the equation, and even then it's not clear. Cotton Mather, who for all intents and purposes seems like a fanatic fundamentalist, was quite happy to allow innoculation against small pox while the physician in town, William Douglas, counter-argued that the town should rely on the providence of God instead of medically intervening. Mather thought that was stupid - the world involved both God's will and medical advancements (in this case). That's roughly what happens over the centuries - there's a level of integration between God and naturalism - and gradually the naturalistic interpretations take over the God's will/providence ones - this doesn't mean that God disappears from the world for Christians, simply that they begin to try to harmonise the two.
I think the real change begins with Huxley (and I'm following Ron Numbers here) who began a specific anti-clerical campaign against the Anglican church and more specifically, argued that empirical, naturalistic science was the only reliable knowledge. Frank Turner said that they sought to
expand the influence of scientific ideas for the purpose of secularising society, rather than for the goal of advancing science internally. Secularization was their goal; science, their weapon. Between Science and Religion, p.16
From then on the issue becomes more more polarized, and here's where looking the Conflict Thesis will help you (it's worth search in this subreddit too). After the advent of Fundamentalism, that's when there is a big shift - Christians don't become anti-science, they become anti-evolution and to be honest, that's about the limit that I've found to anti-science in Christianity (in this case, mostly fundamentalist Protestant churches). There's a couple of Patristics who might be counted as not particularly enthusiastic about pagan learning, but again, it's a few - there are some who enthusiastically embrace it, and that's been the situation ever since.
Probably one event, more than many others, crystalizes the idea that modern Christianity is anti-science, the Fundamentalist-Modernist debate. This event is not on your list of events, but it is one that needs to be talked about when it comes to issues such as the perception of Christianity as anti-science.
Fundamentalists are a loose confederacy of a particular subset of evangelical Christianity. For the sake of ease, and because it is--for better or worse--the accepted definition in academy, a Fundamentalist is a militant evangelical Christian.
Fundamentalism was a reaction to churches that were, from their perspective, accommodating to new, modernist theologies. Seminaries, thanks in part to the work of Ranke, began to teach German Higher Criticism of the Bible. This form of Biblical interpretation questioned the history presented in the text. That it was doubtful, for example, that the world was created in six, literal days. These fundamentalists viewed this as an attack not only on Christianity, but also on the nation. For Fundamentalists saw themselves as something of the moral watchmen and women of the nation, and believed that this was, in fact, a Christian (Protestant) nation. But this should not mask a larger tension in US history, the struggle between professional elites and the Jeffersonian yeoman individual. Some elite seminaries were teaching that there was a proper way to read the Bible and that one must be trained to do so. The Protestant orthodoxy was that one simply needed to read the Bible on their own: sola scriptura, not by methods of biblical interpretation, was the rallying cry of the Reformation after all.
To make matters worse, those Fundamentalists perceived a nadir in the support of Biblical authority. As Sandeen put it, they perceived this point as the lowest support of Biblical authority since Constantine. The Civil War, as Protestants on both sides of the sectional divide, rested their pro- and anti-slavery positions on the Bible, saw a great fissure in the denominations. If the Bible truly did support slavery, then how can anti-slavery or abolitionists support biblical authority as a guiding light for the nation?
Concurrently, Princeton was doing its own thing, and actually providing a defense for that casualty of the Civil War, biblical authority. The Reformed Calvinist flagship was devising its own theology, but it was based on scientific principles. For these Princetonians, the Bible was a factbook. It described the one's relationship with God and proof of how God interacted in human events. It proved the existence of God, for these thinkers, as they applied Baconian inductive principles to the text. It was, like with the development of historiography, the application of science to the humanities. This Princetonian theology won over Fundamentalist leaders. In other words, the Fundamentalists were not anti-science. They were just pro-an-outdated-form-of-science that worked with their beliefs.
Some fundamentalism began to separating from their churches (some continued to stay in even after Scopes). But when the American public seemed like it was on the verge of accepting evolution, espicially after the formerly Methodist Episcopal Church, South's (MECS) flagship university Vanderbilt accepted evolution (leading to the creation of Southern Methodist University), the Fundamentalists knew they could not just separate. They had to take their fight to public schools in order to keep the nation on a moral path. This eventuates in the famous Scopes trial. While the creationists technically won the trial, they lost the PR campaign. The elites laughed them out of centers of learning. But while Fundamentalists lost any elite support they had, they still remained popular. Aimee Semple McPherson, the famed Los Angeles fundamentalist evangelist, was still making headlines, albeit for faking her own death. (For more on if McPherson was a fundamentalist, see Sutton's work.)
However, this does not mean that all Christian were against evolution. The Vanderbilt case should be proof alone. We can see other cases as well. For example, MECS minister Andrew Rice penned his The Old Testament in the Life of Today attempted to reconcile the Bible with evolution. When Rice was up for a position at the new flagship of the MECS, Southern Methodist University, he was barred for joining the faculty. Rather, he went to Tulsa, Oklahoma, and help a fledging church, Boston Avenue MECS. Today, Boston Avenue is a pretty respected, liberal parish in the United Methodist Church.