I can chime in from philosophical point of view, if that's allowed on this sub.

First of all, religion and science are not fixed ethernal concepts, that have run in paralel throughout history and have been fighting for dominance. They are both highly flexible systems, often merged into one, incorporating new findings to previous knowledge (yes, including Christianity). In fact, modern understanding of science appeared in age of enlightenment in 17th century, and we have quite a road ahead with Christianity until we reach Descartes and Bacon.

Christian religion in it's early stages followed Platonism as a continuation of antient world conflict between Platonism and Aristotelianism. Here is a nice short sumary from university of Idaho. This is essential for understanding 'leitmotif' of human approach to epistemology (theory of knowledge) through milenia and is valid even in our time, when we have dominance of Aristotelianism.

Christianity in it's early stages continued tradition of Platonism, or specifically neo-platonism from 3rd century AD. It's represented by greek philosopher Plotinos(204-270), who added several new concepts, that mixed very well with Christianity. Most notably some new mysticism like "extcasy" (yes, the drug is named after this). Extcasy is the idea that "highest knowledge" can only be experienced or lived or seen, there's not even word for it, but can't be "known" in the traditional sense. The most understandable explanation I received at my University was "Imagine wanting to understand what's orgasm by talking about it a lot, but never experiencing one." This is of course our university professor explaining it, and not historical explanation, but it kinda works. We even joked that's maybe the reason why some religious statues look like they are at the edge of pleasure. Imagine being an artist trying to capture something like extcasy.

Another important neoplatonic invention is "The One", which is the collection of all platonic ideals. For Christianity, this was simply God.

I hope we are starting to see paralels and continuation of ancient "science" in early Christianity. It goes so deep that Nietzsche called Christianity "platonism for the masses". But maybe let's leave Nietzsche out of this.

So for Christianity, it wasn't, at least at first, about forbiding some form of scientific knowledge, and enforcing religiosity. For medieval times, those haven't even been separate approaches. They simply believed that by "getting closer to god", you are closer to understanding the true nature of everything, because he encompasses all ideals into one. They deemed their "neo-platonic" way superior. The whole first stage of Christian thinking, Patristic period, is fueled by these platonic ideas, and scientific research is actually rooted in theology. Augustine of Hippo (354 - 450) is one of more well known philosophers of this era. Im epistemology, he used an idea of illumination, where god iluminates rational mind with knowledge.

Then came Thomas Aquinas (1225-1274). Long story short, Aristotle is back. The biggest novelty is that humans can study nature even without divine intervention, and understand a lot of things on their own, as they are made to be that way. His whole epistemology brought in a new wave of thinking, that bears a signs of very early scientific approach, but with a strong influence of church. This led to interesting novelties, like trying to find the proof of God's existence. By logic. Aristotelian logic. Unimaginable with early christians.

For example William Occam (1287-1347), best known for his razor, was practically setting a pillar for scientific method by preferring logical rules for validating multiple hypotheses, not divine ones.

Then came Renaissance, they liked Plato again, but since we're talking about medieval times, that's another topic.

Whole idea that science was suppressed is inherently flawed, as humans always strived for more knowledge, only methods and rationalization of methods have been changing. On the beck of any philosophical rationalisations, there have been constant technological evolution. Best seen in art of war or architecture. In medieval times, science and theology and philosophy haven't been even really separated. Even Newton thought of his highly scientific method as natural philosophy. That's our projection from modern times. "What if" they used some other method for acquiring knowledge in 8th century is such an abstract alternate history thought experiment, that it's unanswerable.

Sory for not providong sources, I don't have them in english language and in my native language are of no use here. If anyone is interested in more, in philosophy we go directly to original philosophers, so read works of those I mentioned. If you want nice quick book that introduced whole philosophy, including medieval ones, in managable form, Gaarder: Sophie's world is usually recommended as an entry point for learning philosophy. It's half fiction book, half retold Bertrand Russell.