The kind of reform you mention is relatively easy to do in Christianity, it is a simiple and flexible belief system: believe Jesus died for your sins, and love your brother. That is about it. It is basic and fundamental and as such, can evolve around any culture.
As people try to complicate it, or mold it into a social system as the dominant philosophy, it tends to fall into corruption and break down. It is not intended to be a political, but a counterculture, an oasis of rebellion against a religious totalitarian regime. That is why it is so different from Islam, which is more like communism, in that they always have the need to expand, "we need more people to be perfect". They work in opposite tandem, Christianity works better when it is is persecution, and Islam works better as a demand to dominate. Interesting, but different.
In Islam, the Koran and Mohammed's example are the main ideal, until they can change these, there is going to be problems dividing politics and religion. Luckily, Christianity works better without politics. Religion and politics should always be separate.