First of all, we must note that these traditional institutions were not always very good at creating stability and security during this time. For example, there was the Hundred Years' War, which devastated France in the 1300s. This was a direct outgrowth of many of the institutions that you mention.
However, if we accept this premise, we can mention the following:
- Religious institutions preached obedience to the existing order of things. This helped to persuade the peasants and other fairly oppressed members of society that they should not rebel, thus helping to maintain stability.
- The political system of feudalism can be said to have helped to provide local security. Each lord was supposed to provide physical security by enforcing the law in his own fief.
- The socio-economic system provided stability by ensuring that each part of society stayed in its own place. It made it so that people knew what their station in life was and knew that they would remain in that station for their entire lives. This is certainly something that would help in maintaining stability.