In an earlier post, I discussed medieval Christianity in broad outlines. But religion (Christianity in this case) is not the same as the institution (the church) whose purpose is to support that religion. This is why, for example, one can still be a good Catholic in the modern world even if deploring some things that some priests have done.
Medieval people made the same distinction. From the middle of the twelfth century on, there were always plenty of people--people who considered themselves good Christians--who mocked priests, bishops, monks, anyone who they themselves did not think was behaving as a good Christian should behave. Wealthy churchmen frequently came in for criticism in the late Middle Ages. Martin Luther's criticism came out of a long tradition.
For that matter, "the medieval church" was not a monolithic entity. One cannot speak of the medieval church any more than one can now speak of the government. (Though some try!) First question: which one do you mean? Federal government? state? local? If federal, which branch, executive, legislative, judicial? If executive, the president himself or the civil service? If legislative, House, Senate, or the staffers? And so on.
In the medieval church, there were many different individuals and groups, all of which had their own agenda. Most notably, bishops and monasteries were often at odds. The bishops had been established by the fourth century in most cities of the old Roman Empire, and they considered themselves to have "apostolic succession." That is, a bishop would have been consecrated by another bishop, himself consecrated by an earlier bishop, and so on, supposedly back to Saint Peter. So bishops felt that cities were their cities, and that they were firmly in the tradition of Jesus's first followers.
The monasteries saw things differently. Although they had been established more recently--rarely before the sixth century in the West and often much later--they believed that they, and only they, were truly "apostolic," because they tried to follow the life of the apostles as described in the New Testament Book of Acts. That is, they gave up all personal possessions and shared everything in common.
(Sounds communist, doesn't it! It's also biblical.)
Monasteries resented bishops, who might live like lords, coming around to "correct" the life of monks who felt that the only person who needed correcting was the wealthy and powerful bishop himself. Monks and bishops did try to get along in a spirit of Christian charity, but monasteries might try to free themselves legally from their bishop's oversight. The cathedral and the chief monastery in a town were often in competition as to who had the best, most impressive church.
And then there were the popes, basically ignored in practice (though honored in theory) throughout the early Middle Ages, until they abruptly made themselves the head of the church hierarchy in the eleventh century (click here for more details).