If you are interested in this topic, you might want to read Hannam's „God’s Philosophers“ as it answers this question more thorougly than I ever could.

To paraphrase: The Church as a whole was not “dogmatically” pro-Aristotle, and their attitude changed over time. In the absence of serious alternatives, Aristotelianism is a very attractive paradigm. Because it seemed well-thought-out and offered a holistic world view it was very embraced both by Muslims and by Early Medieval Christians (as far as the fragmented translations they had during the Early Middle Ages went). Once Christian armies occupied some Muslim territories in Spain and they got their hands on the full body, it partly triggered the Renaissance of the High Middle Ages where it was very influential at the early universities. Personally, I also find it stunning that they embraced Aristotle so quickly. It was not just that Aristotle was pagan; it was also that Aristotle was next to incomprehensible for uninitiated readers except by commentaries that were written by Arabs of all people (e.g. Averroes). And these very same commentaries were the texts that were read by the Christian scholars. Again, the holistic approach of logic, physics and a range of other subjects was very attractive. Especially logic was very important at medieval universities, in part because it enabled skilled speakers to out-argue any opponent with ease, which was crucial, both for questions of religious orthodoxy and personal pride (and both were sometimes mixed).

Now, it is important that there were some frictions between Aristotelianism and Christianity, both on a theological level and on a “scientific” level. The former was e.g. that Aristotle believed that nature could not produce a vacuum, which was taken to contradict God’s omnipotence. Another point of contention was that Aristotle believed the world to be eternal while Christians believed the world to have been created at a certain point (this is not to be confused with Young Earth Creationism vs. Modern Physics. The debate was more or less abstract and metaphysical on both sides. Neither Aristotle nor the Medievals could prove anything).

It is also important to understand that Christianity could easily tolerate “foreign” ideas. E.g. Augustine of Hippo (one of the most important Church Fathers) speaks very warmly of Neoplatonism (unlike his former religion of Manichaeism, which he condemns). But statements that non-Christian philosophers could have stumbled on some nuggets of theological gold or that philosophy is a “handmaiden of theology” only serve for so long. Ultimately a fundamental question needed to be answered: What is stronger, philosophy or theology?

Ultimately Thomas of Aquinas “proved” compatibility of Aristotle and Catholicism, e.g. that reason could not possibly contradict faith, that searching for tangible “secondary causes” for God’s will was a worthwhile pursuit (roughly: “science is good”)… And sometimes he simple disagreed with Aristotle and said that he (Aquinas) believed the philosopher to have erred (Aristotle is only human after all). By this proof everybody could finally embrace Aristotle in a safe way and he became entrenched in Catholicism for centuries to come (well, except for die-hard-Averroes-disciples). At the same time, this solution also resulted in a clearer separation of the realms of natural philosophy and theology. Essentially, “scientific” theories would not have theological implications as they did not stray into the area of faith in the first place, and thus they became non-heretical by default. Furthermore their authors (natural philosophers who did not have a degree in theology) lacked the theological training and understanding to mount serious heresy anyway. At the same time, theologians would not waste their time with mundane natural philosophy and focus on the mysterious of real importance. Furthermore, the Catholic Church banned “fundamentalist” Aristotelianism by saying that it was wrong to claim that God was limited to what Aristotle thought was possible (the no-vacuum-idea from above).

On the matter of (proto-)science (the second area of contention), the thing is that Aristotle is wrong on a huge number of points (e.g. vacuum not only exists, space-wise (NPI) there is actually quite a lot of it). To be fair to him, though, how could he have known?). And as the Middle Ages went on Catholic clergymen and laymen eventually designed theories that are closer to modern physics than Aristotle was, e.g. with the impetus theory or descriptions of magnetism (something that is next to incompatible with Aristotle’s world view).

To sum it up, Christians greatly appreciated Aristotle’s achievement but were aware that he was human and thus not infallible. Therefore, they did not “dogmatically” follow him.

But you are probably really asking about heliocentrism and not boring stuff like the “why do apples fall down?”-impetus theory.

The reason the Church adhered to geocentrism was, that the vast majority of “scientists” at the time believed it to be true and while Galileo could offer serious evidence that legacy geocentrism was wrong, he could not yet really prove heliocentrism (especially not with perfectly circular orbits, as these are noticeably wrong). At the same time, there were issues with heliocentrism from an empirical (“stellar parallax”) as well paradigmatic perspective. For these reasons, the Church did not look too kindly on heliocentrism although it was accepted as a heuristical mathematical model, due to it being much easier to use than the geocentric model, which required convoluted mathematics.

HOWEVER:

The Galileo Affair was about muuuch more than astronomy. It was also about politics, deception, friendship, betrayal, … even before later people started to use it as a surrogate for whatever political goals they pursued. But I think that if you search this sub, you will find ample of commentaries on that episode already.

Edit: Minor clarifications right after submission.

Great question. A complete answer would take up a book, so here are a few points that I think will help explain the phenomenon, as well as its limitations. The quick answer is that Christian thinkers are/were far from dogmatically Aristotelian, but that his appeal has a lot to do with the origins of Christianity and the questions it was facing when Aristotle was reintroduced.

1. The groundwork for Aristotle as a companion to Christian thought is laid first by Platonism, or really, Neoplatonism, which we can insufficiently describe as Plato’s philosophy with some mysticism attached, courtesy of Plotinus. Neoplatonism was very popular among early church thinkers, particularly Origen, Cyril of Alexandria, and the Cappadocian Fathers (Basil the Great, Gregory of Nyssa and Gregory of Nazianzus). Augustine of Hippo was heavily influenced by Neoplatonism, and as one of the most foundational thinkers for Western Christian thought, he is a major place where it is retained. Neoplatonism was popular for being a philosophy which held a strong view of divine unity in its notion the One, or the Good, and who had an appealing cosmology (understanding of how the universe was ordered with respect to divinity) which permitted a notion of a single, omnipotent creator and redeemer of the world. It also has a concept of the logos (Greek: word) which St. John applies to Christ in his gospel and letters. Of course, it was not a perfect fit, and many of its proponents could be critical as well, but it was still a philosophical school with a lot to offer a budding religion in search of intellectual bona fides. More could be said here (again, think of the book that I’m not writing); what is important to note is that many early Christian thinkers are heavily influenced by Plato, and even though Aristotle and Plato have essential differences, much of what they share in common (well, sort of in common) is going to be what appeals to later Christian thinkers.

2. The Aristotle and Plato you know are not the ones most Christians in history have known, due to large body of works which were once attributed to them but are now known to be pseudepigrapha, or falsely attributed writings. The problem of pseudoepigraha is not limited to Aristotle and Plato. At the time of the late Medieval period, more pseudo-Augustine than genuine was read, and biblical scholars have determined that some of the New Testament epistles attributed to Paul are not genuine. Still, it is important to recognize that the Aristotle of the Middle Ages is not the Aristotle of today is not the Aristotle that once lived, whoever he might have been. Adding to this is the fact that Aristotle and Plato were reintroduced to the West around the 12th century. So rather than being a constant, explicit influence, Aristotle comes back onto the scene as something new but also something strangely familiar.

3. While early Christians found Plato appealing because of his concept of the One or the Good and subsequent cosmology, Aristotle was appealing to medieval Christian thinkers, in part, because of his metaphysics. A brief summary: Aristotle held a distinction between what we will call essences and accidents. To understand this, imagine a cup: it has a certain color, shape, height, size, etc. Maybe it has a handle, maybe a lid. Its accidents are all those things you could use to distinguish it from other cups or all those things about it which you could change without it ceasing to be a cup. For example, you could take a red cup, paint it green, and it would still be a cup. The essence of a cup is harder to define, because it is that which all cups have in common, a sort of ideal “cup-ness” in which all cups participate. It is that which makes the cup a cup. Now, we might think this a weird thing for Christian to get excited about, except when we remember that the Eucharist has become more and more the center of Christian worship in the West. Here we have bread and wine which are said to be the body and blood of Jesus, though they still appear to be bread and wine to every bodily sense. Aristotelian metaphysics provided a way to make sense of how the bread and wine could become the body and blood of Christ while still retaining all the appearances of bread and wine to the senses. This explanation is commonly known as transubstantiation, and its proponents argue that in the Eucharist the while the accidents of bread and wine are retained, the essences of bread and wine are removed and replaced with the essences of body and blood. Thus you have a substance which in accident appears to be bread and wine but in essence is the body and blood of Christ. What is great about this is that not only does it explain how the Eucharist is what it is, but it also explains how it is a miracle. For you see, in nature we never find essences changing while accidents remain the same, which is what happens in transubstantiation. You have accidents change all the time while essences remain unchanged (think about painting the cup), and you have both accidents and essences changing (think now about burning a cup to ash; it is no longer a cup in either accident or essence), but never do you have the accidents remaining unaffected when essences are changed. So, in sum, Aristotelian metaphysics allowed medieval Christian thinkers to settle the question of what happened in the Eucharist that both explained the experienced reality and retained the miraculous status. Pretty exciting, right? The thinker who is best known for this fusion the Angelic Doctor, Thomas Aquinas, best known for his systematic theology, the Summa theologiae.

4. The place of Aristotelian thought in Christianity has been hotly disputed, often for the reason your question indicates. The doctrine of transubstantiation was always controversial, even before the Reformation, where Aristotle would find his most notable opponent in Martin Luther. Luther’s philosophical background could be best described as nominalist, and he had a strong dislike of scholastic thought (chiefly Aquinas and those following him). One basic difference between a nominalist and and an Aristotelian lies in whether or not one essences have their own, independent reality. For Aristotelians, they did, while for nominalists, they did not. To understand this difference in thought, consider the difference between bullion and a banknote as currency. The value of bullion is inherent to its material: it’s worth is not merely ascribed to it but inherent to the metal of which it consists. The value of a banknote, however, is not inherent to its materials: a hundred dollar bill is worth far more than the paper and ink used to print it, whereas a penny is actually worth less than the materials it is made with. Nominalists viewed essences is the same way as we understand the value of a banknote: they are not inherent to it but merely ascribed or named, hence nomen (Latin: name) -alism. Beyond philosophical differences (which were not as huge for Luther anyway), he objected to what he saw as the dependence of Christian thought on pagan philosophy which was only used to strip away what should properly be a mystery about the Eucharist. Luther’s objection is part of his strong emphasis on the divine Logos or Word, which I won't go into here except to note ironically that the Logos is a Neoplatonic concept, although again it is also thoroughly Christian. There are other objects to Aristotle, but Luther is a fairly good (and important) example that is helpful to see how Christianity is not monolithic in its thought.

I hope this helps! Remember that these things are complicated, and to take each thinker in stride rather than treating Christianity or Christian thought as a monolith. See a few scattered sources/further reading examples if you have more questions:

Primary:

• On First Principles by Origen, ed. Cavadini (Ave Maria, 2013)

• On the Free Choice of the Will, On Grace and Free Choice, and Other Writings by Augustine, ed. Peter King (Cambridge, 2010)

• Summa Theologiae IIIa.73-83 (i.e. Part III, Questions 73-83)

• “Disputation Against Scholastic Theology (1517)” by Martin Luther in Luther’s Works: American Edition, ed. Lehmann (Fortress Press, 1957)

Secondary:

• Philosophy for Understanding Theology, 2nd Ed. by Diogenes Allen and Eric O. Springsted (Westminster, 2007)

• Knowing the Love of Christ: An Introduction to the Theology of St. Thomas Aquinas by Dauphinais and Lovering (Notre Dame, 2002)

• The Theology of Martin Luther by Paul Althus (Fortress Press, 1966)

• The Harvest of Medieval Theology by Heiko Oberman (Harvard, 1963)

• The Christian Tradition, Vols. I and IV by Jaroslav Pelikan (Chicago, 1984)

This is a great question! Consider crossposting to /r/askphilosophy

I might back up /u/tinrond's answer by quoting Dantes Inferno, which was hugely inspired by Aristotle (he calls him the master of all knowers, describing him as on the throne in Limbo surrounded by other thinkers), in Stanza 11 there is a discussion on Aristotle's Ethics:

Have you forgotten that your Ethics states The three main dispositions of the soul That lead to those offenses Heaven hates –

...

Go back a little further,” I said, “to where You spoke of usury as an offense Against God’s goodness. How is that made clear?”

“Philosophy makes plain by many reason,” He answered me, “to those who heed her teachings, How all of Nature – her laws, her fruits, her seasons – Springs from the Ultimate Intellect and Its art: And if you read your Physics with due care, You will note, not many pages from the start,

That Art strives after her by imitation, As the disciple imitates the master; Art, as it were, is the Grandchild of Creation.

Basically, Dante is saying that human art (which includes philosophy, as well as natural science), imitates nature, which in itself stems from the Ultimate Intellect, aka God.

This is very much in line with Aquinea's "resolution", and it's no coincidence that this bit comes shortly after Aristotle's Ethics is quoted.

More interesting discussion on Aristotle and Dante can be found near the end of this translation.