In Mt 13:33 reports of Jesus: He told them another parable. “The kingdom of heaven is like leaven that a woman took and hid in three measures of flour, till it was all leavened.” Christianity is the leaven of the world. Put it into the world and gradually the whole world is leavened. This is the Christianization of the world.
Note that leaven works from the inside out, not the outside in. Christianization does not mean the world is given a coating of Christianity in hopes that it will penetrate further down. Rather, it means that the leaven of Christianity is put into the middle of the world and gradually works its way throughout.
When this is done, the outside at first may look as if nothing much has changed. But if the inside has changed, then sooner or later the outside and everything in between will change. That is what genuine Christianization means.
Christianity is a meta-religion: it “comes after” religion because it takes a religion and transforms it. The first religion Christianity was applied to was Judaism, as recorded in the New Testament. After that, the pagan religion of the gentiles in Europe was Christianized. Many of the customs associated with Christianity today come from Christianized Judaism and paganism. For example, Easter is a Christianized spring festival (the name comes from the Teutonic goddess of spring) and Christmas is a Christianized winter solstice festival.
Other religions have not been Christianized as much, but they could be. Music is one aspect which has been Christianized. There are Christian songs in every music tradition. Converts from any religion should be able to retain parts of their culture with a new focus and interpretation. Christianity is not about replacing the cultures of the world but about redeeming them.
The kingdom of God is the Christianization of the world. Where the kingship of Christ is, there is the kingdom of God. The world in all its diversity can be redeemed — and preserved — through Christ.