During the middle ages, Catholic monasteries and convents preserved and transcribed old texts to make sure scientific achievements of the past are not lost. They also produced their own scholarships. Not only that, they might be the only people doing this in the western world.
I think it is fair to say that without the Church, western science will look completely different than it is today.
For the Galileo trial, I mentioned this before in a previous thread Follow Galileo or Kepler?
Great article @Patrick. Well balanced, informative, and thoughful:
Flash points and trading zones
Looking back over history, we certainly find many occasions when science and religion have been in conflict. Call these flash points. Among these is the rejection of miracles by those convinced that nature is bound by unbreakable natural laws. Or the denial of human freedom by those who see the human mind as nothing more than the workings of brain chemistry.
In the early 17th century some Catholics found new theories of matter disturbing because of the challenges they posed to their understanding of the Eucharist. For some Jews, the ban on astrology between 200AD and 500AD stifled astronomical inquiry. For biblical literalists, Darwinian evolution routinely provokes an oppositional stance.
On the other hand, we can identify many points of conciliation and enrichment. Think of these as trading zones. Take the biblical idea that all humankind is descended from a single source. This belief inspired the search for the beginnings of human language and for the routes by which early humans diffused across the globe.
In the 17th century, scientific instruments such as the telescope and microscope were conceived as ways of reversing the effects of Adam’s fall from grace. Scientific methods and instruments were devised as a means for ameliorating the damage to human cognitive powers and sensory apparatus believed to have been brought about by human sinfulness.