The Catholic Church's authority during the Middle Ages depends on the area of the world. In Europe, it was practically absolute until the Protestant Reformation, to the point that the lands were often referred to as Christendom.
While this might seem trivial from a modern perspective, it is important to remember how the average peasant's life was during such a time, in which individuals rarely traveled far beyond their hometown, if at all. It was a simple existence, and the Church was a comforting presence, not at considered authoritarian, as it provided simple answers to where we came from, why we were here, what happens when we die and so on.
It is important to understand this reality as it also ties into why the Church was as powerful as it was. This is because of the consequences that could happen, be it to the lowly peasant, a powerful ruler, or even a whole country, if the Church was crossed. When an individual was removed from Church services (excommunication) this basically meant that they could no longer receive baptism, communion, be buried in consecrated ground (among others). To be denied this was to be separated from God, and therefore existence and purpose as most people understood it.
Not only did people fear this fate, those guilty were treated harshly by others due to the behavior that caused such judgment. As disastrous as this was, it could be worse due to the possibility of the interdict, in which entire countries were subject to the above penalties. Given this possibility, it becomes clear why few people or rulers dared to question the Catholic Church and the Pope, its chosen leader, especially as such punishments had few exceptions or forgiveness.