My answer: they were not Christian civilizations, or rather, they were not Catholic civilizations. More specifically, they were not and are not civilizations based on a Biblical understanding of creation taught with and through a uniquely Catholic understanding of Aristotelian natural philosophy. You might say that they were and are insufficiently Dominican! :-)
If you are insufficiently curious about the natural world, or if you see curiosity about the natural world as evil, then you will not venture out to observe and attempt to explain what lies outside the mind. If you see the material universe as a deeply flawed reflection of the True Form of the Universe, then you will come to believe that studying the reflection will only lead to error about the Form. In the same way, if you hold that material reality is not real at all and that only the mind matters in constructing what others call "real," then your study will be limited to the mind alone. Also, if you think that language alone determines reality, then you will see no use in trying to connect how you think about reality with any sort of "reality" beyond the way you chose to talk about it.
However, if you hold that the material universe is a creation of a Divine Mind, reflecting this Mind's desire for order and intelligibility, then you will venture out to discover and explain what lies outside the human mind. If you think that you can come to know the Divine Mind better by exploring its creation, then your scientific explorations become not only a professional duty but a religious one as well. Believing that creation participates in its Creator serves the highly innovative purposes of discovery and invention. Believing that you will be improved, enriched, and ultimately redeemed only fuels your natural curiosity.
Some will say that capitalism and democracy contributed to the growth of scientific knowledge in the west. This is certainly true. However, capitalism is a late comer to the world scene of science and democracy in its ancient form was little more than mob rule. Let's not forget that the scientific advances made during the Enlightenment were made possible by a medieval theology of creation. The idea that the medieval Church punished scientific research is nonsense. Almost every scientific discovery and innovation of the Enlightenment can be traced back to a priest or religious living during the middle ages. Conflicts between scientists and Church authority occurred when scientists played at being theologians.
In the modern age, atheistic communism and religious fundamentalism have been the true enemies of science. Need we review Mao's disastrous Great Leap Forward as an example? Or Stalin's collectivization of rural Russia? Or the sorry state of scientific research in Islamic countries? Christian fundamentalism has never held sway over a nation like fundamentalist Islam has and still does. The widely publicized battles over evolution in the US have not seriously damaged scientific research in this country. They have had no effect in predominately Catholic Europe. The danger to a truly advanced science in the west right now is fundamentalist secularism--science as technology without an objective morality. Combined with a "progressive" and materialist view of the human person, secularist science serves an elitist design for manipulating creation without its Creator, without reference to ultimate purpose or transcendent ideals. This means one thing: power. Potentially, unchecked power.
Thus the need for faithful Catholic scientists and theologians schooled in science. The Church has nothing to fear from a scientific method that works under the rubric that it is creation that's being studied. . .not just a physical universe without purpose or design.