There is no state in Medieval Europe, with exception of Byzantium and proto-state in case of Carolingians. Medieval Christendom is anarchistic civilization.
No state === anarchy. And no state church.
What makes sense is speaking of ruling class which can't unified and therefore can't enforce same policy. Look, kings/emperors wants more power, nobles want same, church depends. So they all keep each other in check and nobody can monopolized legitimate force usage.
Church can't increase temporal power because nobles (which form army) are against it, while king/emperor can't increase spiritual power due to alliance between pope and nobles. Situation is stalemate.
Which results in variants on theme local beliefs since laws are local and enforced locally.
Martin Luther is proof. Both Emperor and Pope ordered him to show at court. Luther has found protection at one of imperial elector who said: Nein. If HRE was state, Emperor's army would be able to arrest Luther. But since HRE isn't state, they can't arrest.
In fact, both Emperor and Pope can only cry. If they try something, their army would risk being gangbanged by 11 armies!. Yes, number is correct. One army is of HRE under control of Diet and there are 10 imperial circles which are responsible for self-defense and can raise armies. Army under Emperor's control is called Imperial army.
en.m.wikipedia.org
en.m.wikipedia.org
en.m.wikipedia.org
Again, if several institutions or groups of people can independently raise army, there is no bloody state. State = monopoly on force == only state can raise army
Which means medieval society used different armies to keep "power in check", while modern states hope to keep different departments of same organisation fighting. Which implies Christendom is way different society that current one and using "modern intuition" how stuff works is misleading.
For example, disobedient noble can't send to supreme court stuffed by politically correct judges. Why? Because there are several different court systems so finding "correct" one will take time. And no court system can incentive to give up case. So king can order time in dungeon, while other independent courts can other release.
So it's military action then. Without cannons there is no way to easily force into castle, so it's siege till starvation. And nobles may not show up to spend summer besieging some castle because king can't bring himself to negotiation. If fact, they may decide they need new king instead of current idiot on throne.
EDIT: Added sections on two occasions.