The place of science in our society should be where almost everything deemed important is, but with the same restrictions. Mistakes start occurring when science is treated as an absolute or as something that is totally unalterable. That same thought pattern, when related to religion, is called "dogma", and it has the feature of slowing the progress that could happen.
It has been proven time and again that science is not absolute, because it depends on our understanding and perceptions. When we come to truly understand this and to look at science with an air of humility, science becomes a very powerful tool for moving forward, without making assumptions and without ego. But if we do not use that distinction, it amounts to the perpetration of myth and misconceptions.
Science is a tremendous tool to acquire knowledge, if it is used properly. For that reason, it is not only valuable, it is necessary. It is almost inescapable, unless a person lives alone on a desert island, and even then, the hint of science pervades if the person wishes to survive. As a wise person once said, "If you go through a day without learning something new, you've wasted an entire day." Science is the means and catalyst for learning.
How does this relate to society? Society can either move forward through knowledge, or lapse back to a time when men were much more superstitious, cautious, and even paranoid. Since science is the harbinger of knowledge, the question becomes, "How important is knowledge in our society?" Given the options, I don't think it is hard to see that it is very important. Again, though, only if the science is approached in the right way and with an open mind, is it truly valuable.