The primary contribution of Christianity to medieval civilization, may have been, in my opinion, the reestablishment of strong family bonds. During the Roman empire, the family had become atomistic.
In Greek times, again in Roman times, and again in post-classical times, the predominant type of family evolved from trustee to domestic to atomistic.
The Trustee family occurred in the earlier stages of civilization, whenever and wherever neither the state nor the church ruled the family; the family ruled itself. In the trustee family, the family embraces many households. One man is head of the family but he is subject to a family counsel and occasionally to the entire family when nearly all members feel so strongly about an issue that they are willing to oppose him.
Trustee Family mores include: men do not openly engage in premarital or extramarital sex. Women do not engage in premarital or extramarital sex, except for the ever present few blacksliders. Women who are not virgins cannot marry and are kicked out of the family. Adulteresses also, or killed if caught in the act.
Property is held in common, is received from previous generations and is held in trust for future generations. The family takes care of its own. It is responsible for seeking revenge or compensation for injury to a family member by an outsider; it is responsible for paying compensation if a member injures an outsider; costly feuds can result.
The domestic family evolves to facilitate commerce. The domestic family is like the individual household in the trustee family. There is no longer a head of family except within the household. Property is no longer held in common or in trust, but can be bought and sold. The family no longer seeks revenge or pays compensation; family members are now subject to the civil power as regards injuries to or from any other individual. The family mores remain as in the trustee family.
The atomistic family puts individualism above family. Men openly visit prostitutes and keep mistresses. Fornication is common. Divorce is common, and easy, and marriage is casual. Children are few or none or neglected. Deviant sexual behavior is common. Abortion is common. Children do not form strong ties to family, therefore to nothing else either. People without strong ties are easier to rule, but they do not form a support for the nation; the nation is easily subjugated by outsiders. Greece was easy prey for Rome when its family structure became atomistic. Rome was easy prey for the barbarians when its family structure became atomistic.
After the fall of Rome, the trustee family structure reappeared in many places, and the Christian church vigorously promoted the domestic family structure to replace both the trustee structure and the atomistic structure.
Zimmerman, Carle C. 1947. Family and Civilization. New York and London: Harper & Brothers, 829 + x pages.
What a great question. There will be so many great opinions, I am sure. I am also sure that there will be many different valid perspectives. Keep in mind that what is "primary" to one person is not always "primary" to another. Let me offer a few points. First, the church offered a alternate base of power. In other words, the church could at times challenge the government. The popes were extremely powerful in the middle ages. Second, the church was the catalyst for education. This point should not be under emphasized. This is one of the great contributions. Finally, the church acted to preserve western culture.
A very important contribution of Christianity as an organized religion to society was in organizing the people and in placing a structure within society to which worshippers could be expected to adhere. This helped the State to impose rules, regulations and even laws. Many accepted without question the idea of the divine right of kings and therefore that every one had his place in society and should stay within it. Church and state roles and positions were often inter-related so therefore the faithful gave much respect to religious officials and followed their guidance in political and social matters. Although society was calm and docile as a result, it didn't really allow for free speech or for the ordinary population to have say.