I have been reading Cox's The Future of Faith. There seems to be a rash of reinterpreting what Christianity means. I don't know if there is a direct-causal relationship, or which way the causality goes, but I will say that the rise of "reinterpreting Christianity" seems to match, almost step-for-step, the rise in theistic evolution among evangelicals. I think that what is happening is that they stem from a common theological sea change - the move from an emphasis on special revelation to an emphasis on general revelation.
Cox describes what he views as the direction that Christianity is headed in as "the age of the spirit". He says that we have been in the "age of belief", where Christianity was identified by adherence to specific doctrines, and are moving into a period where Christianity will be defined by people who are empowered by the awe they see in the universe, however they define it, to live it out in their lives by doing good.
Cox tried to make a connection to this view of the world to the early days of Christianity, but really it doesn't stack up. The Bible - the book produced and used by the early Church - makes it clear both that (a) there is doctrine, and (b) that it is important. It is true that sometimes Christians go overboard with doctrine and forget our calling in the world. Nevertheless, scripture (and likewise the early Church) makes it clear that doctrine is, in fact, important. Of course it is wildly popular today to talk about other types of Christianity in the early period (Paul had some interesting things to say about these other types of Christianity himself). However, this was not mainstream Christianity, nor was it an extension of the apostle's teaching.
The fundamental flaw with the move to general revelation over special revelation is that Christianity is a historical religion. It's very foundation is the fact that God has indeed done special things throughout history. God is Himself involved in history. Christianity cannot be replaced with a sense of awe that invokes a desire to do good. It is about God doing specific things with specific meanings.
Did God do these things? If so, then they matter - both their historical reality and their implications. If not, then we need to not improve Christianity, but rather simply switch religions.
Cox on several occasions tries to convince the reader that the old way of believing is invalid, but his arguments are excessively weak. He argues against end-times notions on the basis that it doesn't help environmentalism. He argues against Biblical Christianity on the basis that Catholics and Jews have different Bibles. He argues against fundamentalism on the basis that people get carried away with it (has he never read any of the liberation theologians he espouses?).
It is true that Christianity is often suffocated by creeds. But the fix is not to abandon them, but to rather, (a) be more cautious about our own ability to fully rationally understand and articulate the faith, and (b) put them in their right place within Christianity. Creeds are important, but God calls us to be united. Cox, like others (see Spong, for instance), call for a "shift" in Christianity, which is actually an abandonment. What you believe is important, because these are God's acts in history. If Jesus did in fact come down to be a sacrifice for us all, then what you believe about that event matters.
The God that Christians worship is a God who has been active in the world from the beginning - not in some nebulous manner - but a real, active, and detectable presence throughout history. Christians live in continuity with God's message, believing in His works, and trusting Him about what the future will hold.
But that is not the future of faith that Harvey Cox sees.