We're not talking about a few centuries ago because science advances exponentially. If you want to go back that far, then I can make the same argument then as well. Four hundred years ago, the best science had to offer was to protect yourself from the plague by bleeding out with leeches and not bathing, and to drink herbal preparations to abort pregnancies. You have to compare apples to apples. Science and religion have only directly competed, in the way that we're talking about now, for the last 75-100 years. You can use Galileo as a counterexample, but even during Galileo's time, a large number of people could accept a heliocentric model and it didn't have the same fundamental hatred as modern religion does for, say, evolution or quantum mechanics.
But what you're saying is that life is better now because of science, yes? I completely agree. But there's a tremendous downside that's overlooked, and if you mention it you get called a "Luddite" or a "technophobe." Sure, our Science has invented great things....we can watch political speeches on TV from anywhere on earth, instantly. But, we can also watch five different versions of Law & Order. We have unprecedented access to medical information, but an entire field of brand-new of highly questionable mental disorders exists because of it: "cyberchondria", ADD, ADHD...these things didn't exist 50 years ago. Why? Was it because people didn't recognize them and better research has discovered it, or is it because they're not actually the problem that people are making it out to be? ADD, for instance. There's a convincing, and growing, body of evidence that 1) cases of ADD are exaggerated by a factor of 10 to 100, 2) ADD is caused by Science's modern lifestyle and 3) what people used to call "being a kid" is now simply assumed to be a mental disorder.
People, cultures, are spiritually drained. My generation (I'm 26) is almost synonymous with "disaffected". Gen-y is renown for its lack of caring about anything significant other than ourselves. Note that I'm not equating "spiritual" to "religious". This modern cult of Science has taught us that we can find the answers with a better brain scan, a deeper MRI, a broader genetic map. It's given us the ability to extend our body physically to 75, 80, 90 years old....but not our spirit, our human-ness.
The OP was saying that religion was standing in the way of science, implying that pre-screening diseases out of children was good. Is it? That's an argument for another day. In the broadest sense, I agree...it is good, IF we can prove a solely genetic link between disease A and a series of Punnett squares. But lets be honest...genetics is still in its infancy, and it's nothing more than hubris to think that Science has determined enough of the human genome, reliably, to pick a combination more valid than it's own holy grail, evolution.
So is ADD and theoretical genetic susceptibility to disease the same as your left-handed or poor? Have we, as a culture, placed such high value on the Science cult that we now completely overlook what generations before believed/knew? For example, chemical and food science has created the most effective delivery mechanisms for calories and nutrition in the history of mankind, and our food supply is well stocked with it. At the same time, computer, business, and management science has reduced the amount of work people have to do to where "going to work" today is nothing like "going to work" was even 30-40 years ago. Result? An obesity "epidemic" in the western world.
Of course, our great--great grandparents would laugh at us, because they knew 100 years ago what Science is just "discovering" now: if you eat a lot of calories and junk food, your ass has to get outside and work. Eat to live. Oddly enough, that's what the Bible, Quran, and basically every other religious text will tell you: eat to live, don't be a glutton, and value a day's work. So there you go...spirituality would have solved the problem, except that Science got in the way.
