This is very different from ecumenism, which attempts to sweep conflicts under the rug and results in a belief-oriented religion whose beliefs are vague--a very thin soup indeed. In an experience-oriented religion, however, it is possible to be quite passionate about one's own experiences without rejecting or belittling the experiences of others. The states of enlightenment achieved by Hindu mystics do not contradict the raptures of Christian saints--both are important examples of the human experience of the divine, and the practices that lead to each are well worth studying.
As an example, let us consider just how much of Christianity could survive inside the next religion. Practitioners of the next religion could contemplate the story of Jesus and meditate on the vision of a personal, caring, self-sacrificing God that is implicit in that story. Many of those who did this would no doubt have the born-again experience, that powerful experience of being in contact with a being who sees to the inmost depths of our souls and loves us unconditionally. The security that this love provides could give them the courage to look at the flawed portions of their lives and to change them, as so many Christians have. They could practice the communion ritual, pray regularly, and attempt to follow the example of Jesus.
What would they not do? They would not attach significance to the Christian belief system as a thing in itself. They would see the significance of the Bible in the experiences that it inspires and the wisdom that it captures, not in its scientific or historical accuracy. Even if it could be conclusively shown that Jesus had never existed, they would not be threatened and would have no need to deny whatever evidence had appeared. They would have experienced what they experienced, and whether the character who inspired those experiences was historical or fictional would make no difference to them. Similarly they would not feel bound by other people's impressions of Jesus or the words attributed to him by ancient writers. To the extent that the various accounts of Christian experiences coincided with their own, they would feel a sense of comradeship, but when those accounts differed or went off into realms that their own experience did not, they would take it with a grain of salt.
My personal opinion is that many Christians will be more comfortable in the next religion than they are in their current churches. They will find that it is the experience and practice of Christianity that is attractive, but that its claim to be a universal theology is simply baggage for the experience and practice to carry. In addition, by focusing on their own experiences Christians would reclaim the Bible for themselves, and take it back from the historians, archeologists, and linguists.
Examples like this could be multiplied at length. Jews, Buddhists, Moslems, and Wiccans alike will find their practices welcomed and their experiences valued in the next religion.