I think it is largely reactionary and the biggest factors are extremist non-believers, who frankly have gone to genocidal extremes (a good example being Mao Tse Tung). There are atheists who are just as eager to jump on evolution as a “proof” God does not exists as there are theists eager to jump on the fact that the universe had a beginning as a “proof” God does exist. The hostile approach of such as Dawkins and Carl Sagan co-opting science as something “on their side,” has only inflamed the irrationality on both sides. Before them it was others like the social darwinists who created this anti-science reaction.
Begin by defusing the reactionary tendencies by making it clear that there is a big difference between science and naturalism. It is probably a good idea to acknowledge that some of what science discovers is likely to make some changes in our beliefs about God and the universe, but while we may have to rethink a few things, this is no reason to throw out everything.
I also think it is likely to help to broach science topics in sermons or bring in visiting speakers who make connections between the findings of science and issues of faith (correctly).
Not very well. My patience is definitely a little bit frayed in that area.