Something worth bearing in mind when you say that the findings of Galileo and Copernicus were "held back for years", is that Galileo in particular did not "find" in the strictest sense that the Earth went around the Sun. He deduced it, based on the logic that, as his moons went around Jupiter, so did small things orbit larger things. This contradicted the Church's model, of course, but also did so with no direct evidence. Ironically, the trial appears to have centred on the relative scientific merits, as they were understood at the time. This is not to say that Religious considerations did not enter into the debate, and had a far greater role than they should, but that was the way of things, and Galileo wasn't straying away from using the religious arguments either. A further point is that he was invited to put his case forward, in a neutral manner, by the pope. Unfortunately, Galileo uses the name "Simplicio" to represent the church's viewpoints, and then makes him simple and intellectually incompetent. Ultimately, Galileo's viewpoints were suppressed because he insulted the Church, rather than just because he disagreed with it.
This is just one case, and can be rationalised as I outlined above, but in general religion has probably been a hindrance to progress -- most starkly when Darwin formed his theory of Evolution and then voluntarily suppressed it for 20-odd years because he knew how religiously controversial it was going to be.