The Feudal system was the best system of government known to Europe during the Middle Ages. It had a system of politics, a system of religion, very basic education, a military, simple currency, and social classes. Though it was considered perfect then, it still had flaws. Many changes needed to be made to the medieval society in order to produce a modern society.
Feudalism had the Pope, a religious leader, at the top of the power ladder. This meant the society was a theocracy. A Catholic theocracy gave advantages to one religion, but many disadvantages to another. If a Jew, Muslim, any nonbeliever, or a heathen lived under this system, he did not have any religious or political protection. Basically, if a Catholic kills the nonbeliever and takes his land, the Pope would not punish him. The most probable reaction from the Pope in this situation is one encouraging that action because it "rids the land of heathens."
If religion and state get separated, the Pope will not be allowed to do that and the commoners are more protected.
A good modern society is one where people were free to practice any religion, and still receive the same protection, treatment, and freedoms as a person who practiced any other religion. The theocracy back in the Middle Ages only granted protection and fair treatment to ones who practiced Catholicism. In other words, one was forced to be a Catholic if he still wanted to live. This type of government violated many people's civil rights and needed a change.
A solid justice system is a perfect amendment to Feudalism. Mainly the clergy dealt with crime and punishment. At the end of a prosecution, the most likely punishment was either pillory or ex-communication, which was considered even worse than the death sentence...