Overall, any dogmatic system of belief will tend to retard scientific progress, because science depends on freedom of thought, ie following a chain of thought where the logic leads, without fear of contravening some prohibition. Nowadays science itself is treated as a religion, and scientists are treated like priests were treated in medieval times, ie deferred to without question, but also expected to have the answer to every problem. Real scientists don't take this attitude, it's more people who "respect" science without having actually studied it. Also, politicians (very few of whom are scientifically educated) use scientific evidence when it backs their proposals, but ignore it when it does not- just as kings used religion in former times.
There is no such thing as "the Church" unless you belong to a specific church that is so bigoted that they don't accept any other churches as being real Christians. Even in Medieval times there were the Catholic and Orthodox churches, plus many other small groups who worked in secret due to being classed as heretics by the big two.
Finally, you have to distinguish between "The Church" as an institution (or group of institutions) and people who happen to be members of a church. Same goes for other religions- those who favour Islam often quote the great Muslim scientists of the Middle Ages, who were far more advanced than Europeans of that period. However this has more to do with the fact that Muslims had conquered several areas that had the longest history of civilisation, eg Egypt, Mesopotamia, Persia, India, and the Eastern Roman Empire. If Muhammad had been a Viking and his warriors had conquered Scandinavia and Germany, it would have been a different story.