Qcmbr + designs:
This notion that science and religion are at opposite ends of a spectrum is a total canard and most science historians no longer advocate this view. You can start off by reading about the conflict thesis on Wikipedia. As the article's intro says:
Events in Europe such as the Galileo affair, associated with the Scientific revolution and the Age of Enlightenment, led scholars such as John William Draper to postulate a conflict thesis, holding that religion and science conflict methodologically, factually and politically. This thesis is advanced by contemporary scientists such as Richard Dawkins, Steven Weinberg and Carl Sagan, and proposed by many creationists. While the conflict thesis remains popular for the public, it has lost favor among most contemporary historians of science.
Unfortunately it's a popular meme among science enthusiasts because it pits them in an "us vs. them" battle against "dumb" people and makes them feel better about themselves. The reality is that the facts do not support this black-and-white view; it's not even shades of gray so much as a needless extrapolation from isolated, misunderstood events.
Religious beliefs have hardly had any effect on scientific curiosity throughout the ages. This cannot be repeated enough. Most scientific discoveries in history were made by theists (there were hardly any atheists in existence for most of history, so this follows naturally). We would not have cured more diseases and established moon bases by now if there were no religion.
Humans are animals who scarcely use the brains they have to get by. When their belly is full they are complacent and lazy. Furthermore, the average person has not the slightest capacity for scientific work. Scientists are the intellectual "1%". They have always been psychological outliers due to their "strange" obsession with understanding things that don't seem to be particularly relevant to putting food in one's belly for the next week.
The only limiter on scientific advances, therefore, is the bell curve of intelligence. People born without a lot of intelligence do not have a yearning to use what intelligence they have to contribute to the sciences. Those who are born with it know what they have and naturally want to use their talents just as an athletic person naturally enjoys using their physical abilities. The upper 3-5% of the IQ range is where scientists lie, and religion has nothing to do with this IQ dispersal. It's just what evolution has set for us. For most of human history it was not very useful to be brilliant, when the main concern of the group was bringing in enough of a harvest to last through the winter.
So don't blame religion; blame the fact that, as animals, we are designed to meet our basic needs and little more. Evolution has experimented with our species by making us intelligence specialists (dialing up our IQs and lowering our basic physical toughness), but since the goal was simply to give us a survival advantage, we shouldn't expect that we will automatically all have a yearning and ability to accomplish incredible scientific feats. Our entire civilization is built upon the backs of a few outlying freaks with exceptional minds. Without them we'd still be living in caves or huts, or maybe primitive villages at best.