The folly of calling for a reformation in Islam comparable with the ‘reformation’ in Christianity lies in the different sources of authority in the two religions.
In Islam, the source of authority is a single infallible book, which is considered by many Muslim scholars to predate the existence of the earth. This book explicitly claims to be infallible. It explicitly claims to be the direct word of God. It reiterates these claims often and at length. Any reformation of Islam must return to the Qur’an, which is fixed and immurable. The moving finger has written and moved on, and nothing can be changed. A Caliph has no authority to add anything to, or take anything from, what is written. His is primarily a political role, and he cannot chose to adapt Islam to suit changing conditions. It is as it is: take it or leave it. Even the tradition, or hadith, those few extra doctrines not found in the Qur’an- such as the idea that Muhammad was the last, the seal of the Prophets- is a closed canon, and has not been augmented for a thousand years.
If you were going to reform Islam, you could plausibly take a look at the Qur’an and make a serious effort to determine which suras might be supplanted by other ones. The logical way to do this would be to take the later, less-tolerant Medinan suras wherever they conflicted with the earlier, more-tolerant Meccan ones. I doubt this is what Janet Albrechtsen has in mind. This will result in a harder, fiercer, less flexible religion, which up to a point will be able to resist the modern world, but it will not be in any way a reformation which will allow Islam to adapt to the modern world.
Another thing you could do is reject the hadith, and go back to the Qur’an alone. In itself this is going to be an entirely negative reform. It can only become positive and adaptive if, in rejecting the un-Qur’anic idea of Muhammad as the seal of the Prophets, you allow a new Prophet to come in with additional teachings expanding on those of Muhammad. This is not a new idea. This is what the Druze did, and the Baha’i’s, and a number of other religions, all of which have in common the fact that through this reformation they are no longer Islam. This path will not result in a reformed Islam, simply in more daughters to join the family of Abrahamic religions.
In Christianity, the ultimate source of authority is a person. Historically, this has been understood to be mediated by an unbroken chain of personal contacts linking the hierarchical Church to the historical person called the Christ. This person never wrote a book, not commanded that any book be written about him. Many things were written about him and his teachings, nevertheless, and were collected by the Church, but these writings do not claim to be infallible, do not claim to be the direct word of God, and as they contradict each other in many places rely on the interpretation of the insititution which originally collected them. The hierarchical Church has historically claimed the power to bind and unbind: to preserve and defend a certain core of dogma, which may be extended from time to time, and to supplement it with a penumbra of disciplinary laws which can be, and are, changed from century to century to adapt to changing conditions.
Now, Christianity can and has been reformed in any number of ways, because reformation seeks to go back to the person who is the ultimate source of authority and express his will in a way which is suited to particular conditions. The hierarchical church is an intrinsically adaptive and reforming institution. On the scale of a human lifetime, it may seem as inflexible as Islam, but on a time scale of millennia you can see that it is alive.
Of course, if you want to have a ‘Martin Luther-style Reformation’, you want to reform Christianity by going outside the traditional means of mediating authority. You need to come up with something besides the hierarchical Church. Luther, having the example of Islam before him- Hungary was on the ropes, and the legions of the Sultan were marching towards the heart of Christendom- seized on the idea of a sacred book as a source of authority. Thus, he took the New Testament, a book far less suitable for such a purpose than the Qur’an or the Torah, and set it up as an infallible authority. This has been shown by events since to have been a dumb idea. Once extracted from its original context, the New Testament has given rise to a bewildering medley of sects that have almost nothing in common, because it does not have the properties of an infallible sacred book that the Qur’an has. It does not answer all the questions that need to be answered. Martin Luther’s ‘reformation’ was a catastrophe for Christendom that left us open for the cancer of moral relativism that has destroyed Western Civilisation in its ancient heartlands. But, I am getting off the track and indulging in gratuitous Prod-bashing. What is important is that it is not possible to do anything remotely analogous to what Luther did in Islam. You cannot extract anything other than the Qur’an as the ultimate source of authority without ceasing to be Islam.
There is only one way to reform Islam that I have thought of. There was once an institution somewhat analogous to the Papacy in its capacity to define and extend dogma, but it was not the Caliphate. It was the Imamate, as understood by the Shi’a, and it ceased to exist many centuries ago with the disappearance of the 12th Imam. Thus, if we truly want to reform Islam- not just open it up to the same postmodernist cancer that has infected Christendom- we need to do two things. We need to support the ascendancy of Shi’a over Sunni, like the United States has been inadvertently doing in Iraq, and we need to hope that the 12th Imam shows up soon.