If one wants to defend the statement that Christianity influenced the emergence of natural sciences, one big question has to be answered:
Why did empirical science take off in Europe only until 1500 years after the birth of Christianity?
This is an essential question. I will try to outline an answer below.
We Had a Fairly Good Start, Though
According to a Finnish scholar Päiviö Latvus, Christianity stimulated the development of natural sciences already in ancient Rome, but the development was abruptly interrupted. At that point, when Christianity became the accepted religion, and later the state religion of Rome, the focus of Roman civilization was moving to the eastern part of the empire: Greece, Asia Minor, Syria, Palestine and Egypt. This is reflected in the development of Christian theology so that all major councils were held in the east, and the most famous theological schools were there as well (Cappadocians, Alexandrians). Although the scientific development during the Roman empire was relatively poor compared to the golden age of Greek philosophy, Latvus finds one salient exception: Philoponos. He criticized the views of the traditional authorities – Plato and Aristotle – on for instance gravity in a manner that preceded many great minds centuries ahead.
Europe and the Migration Period
After the modest beginning of the development came the Migration Period. Thomas J. Craughwell has written an excellent book “How the Barbarian Invasions Shaped the Modern World” which I read recently. The Barbarians more or less literally wiped off the ancient world and left behind only smoking ruins. Europe had to rebuild an entire world from scratch. The city of Rome was sacked at least by Gauls, Visigoths, Vandals, Ostrogoths, Arabs and Normans. It might be somewhat hard to do science, when your children starve to death, women are raped and cities burnt.
In popular culture, the Dark Ages often are associated with the Pope's jurisdiction, strict church discipline, corruption, superstition, the Inquisition, witch hunt and so on. The Catholic Church is said to have controlled virtually an entire continent. Although some of this is true, there were many occasions when Europe was actually significantly weak, surrounded by more powerful enemies and not at all coherent or unified by the horrendous grasp of the Holy See. By contrast, there was a time when the world's largest church was neither the Catholic Church, nor the Eastern Orthodox Church, but the Nestorian Church. It was spread to Persia and its missionaries traveled all the way up to Mongolia. Meanwhile, the map of Europe was filled with people wandering across the continent: the Vikings took possession of England, Northern France, Scandinavia and much of the current Russia. Spain was almost entirely held by the Moors, Byzantium ultimately only a strip of northern Turkey, until it completely disappeared from history. The Islamic ummah had spread throughout the Christian territories by the Mediterranean, except for France, Italy, the Balkans and Greece. Russia was completely pagan until the reign of Prince Vladimir of Kiev.
The Turn of the Tide
When the Vikings finally converted to Christianity and ceased to terrorize the Atlantic beaches, the Crusades started to draw the scarce resources of Europe to the Holy Land, the Black Death raged killing third of Europe’s population, the Mongols rode with their horse-powered armies up to the Adriatic Sea (after slaughtering incomprehensible amounts of people) and a few hundred years later, the Ottoman emperor Suleiman was knock-knock-knocking on the gates of Vienna with his janissaries.
However, the sultan was defeated in 1529 and gradually pushed back to Turkey. In the meantime, and partly because of the Turks, the Reformation could start without as much interference by the Vatican as otherwise would have been probable. In this world shaped by the Reformation - Protestant Northern Europe - natural sciences began to evolve at an increasing speed.
The Material Development Provides Resources for the Intellectual
Above is only a fast and rough overview of the historical lines I consider essential, but I think it points out what kind of miseries troubled Europe for centuries. The plight affected materially and socially: the status of child and woman improved substantially only until the influence of the Fransiscans, who are considered sometimes as one of the “pre-reformator” movements. This status is important in early human and psychological development of the intellect. Therefore I argue tentatively that the Migration Period disrupted the development of natural sciences, and this development was not able to continue before the Reformation. An intellectual development was not the only required factor, but also a material and social development needed to be catalyzed. It cannot be underestimated that Europe had to be built again after the collapse of the ancient world. This did not happen overnight.
On the other hand we must also remember that there are inventions and intellectual principles that do not immediately affect people's daily lives and thus do not contribute to the upbringing of a new, larger generation of potential scientific minds, however revolutionary they may ever be. Other discoveries in turn, harness the forces of nature to produce unimaginable wealth and prosperity. From this perspective, the speed of the development is not as interesting a question. The real wonder is that natural sciences in their current extent exist at all.