I don't think that modern religion and science have much bearing on each other at all. Historically sure, but these days nope. Modern religion has to deal with the fallout from new scientific advancements, because they bring up new moral questions that had never come up before, and they don't always deal with it very well very fast, but religion itself is not about science.
Hang around the modern Muslim countries a bit. Most of them view science very highly (Not the backwards extremist ones that lynch gays and are used as anti-Middle Eastern propaganda)
I know a lot of people who actively teach children that Allah values knowledge more than wealth. Many Muslim country leaders try to use the policy to motivate rural people to get into science and modernize the countries. Religion is indeed a very powerful motivator, I know quite a few people who become scientists mainly because it gives them piety points.
Theologically, Islam puts every human as a Khalifa (representative) on earth, and their role is to protect the world, and become leaders. The Islamic version of the Adam and Eve story is that Adam was created to expose Satan as a rebel. Adam was given knowledge of the Earth, Satan refused to bow in respect to him, and was kicked out. This put knowledge as the highest pillar of respect in Islam (and that includes scientific knowledge, not just theological). Knowledge was what makes humanity superior to animals, angels, and devils.
It's questionable how much religion factors in, but in a modern Muslim world, science garners a lot of respect.
Note that, with very little interpretation, it can be shown that the Koran talks about the Big Bang and quite a lot of other theories. This denies evolution, but acknowledges the validity of the theory. (I do not have the familiarity with the Koran to do this. It was shown to me by a Muslim cleric i was working with, and it made a lot of sense, but I can't reproduce it.)
With regards to the original thread subject, the only time in the history of Christendom where scientific progress was largely stalled had little to do with religion, and almost everything to do with the constant warfare caused by the power vacuum left by the collapsing Romans. Some individual theories
have come under fire through the ages, of course, but that's quite true of any power centre, including secular or even violently atheistic ones. As for superstition and mysticism, not only was that rarely part of Church doctrine, for much of the time, it was actively
opposed by the church. If, for example, you tried to denounce a neighbor to the Spanish Inquisition for witchcraft, YOU would be thrown in jail for fearmongering.