Source: Qur'an (Koran) as shown at http://www.hti.umich.edu/k/koran/ and elsewhere.
The theological basis for the prosecution of Rahman apparently comes from a misreading of Qur'an 16.106, which says, "He who disbelieves in Allah after his having believed, not he who is compelled while his heart is at rest on account of faith, but he who opens (his) breast to disbelief-- on these is the wrath of Allah, and they shall have a grievous chastisement."
Immediately we can see two theological errors in prosecuting Rahman on this basis: First, he is not "disbelieving in Allah." Allah is the creator of the universe, and there is only one Allah. We Christians call Him, "God," or "Heavenly Father." But we are talking about the same One Creator, who has revealed Himself to different people in slightly different ways, for His own good reasons. As a Christian, Rahman still believes in Allah, as do I myself. And second, the "grievous punishment" is supposed to come from Allah Himself, on Judgment Day, not from fallible humans today. Furthermore, everyone should keep in mind that all punishments specified in the Qur'an may be moderated and reduced by applying the oft-stated principle that "Allah is forgiving, merciful," as stated in Qur'an 2.173 and seventy-six other places in the Qur'an. Allah knows your heart. In Islam, if you have a really good reason, Allah will overlook or forgive almost anything.
So we see that the prosecution of Abdul Rahman in Afghanistan for converting from Islam to Christianity, in supposed violation of "Islamic law," is itself a violation of Islamic law, the highest written authority in which is the Qur'an.
In Islam, there are some secondary written authorities called the "hadith," or "sayings," attributed to the prophet Muhammad, some of which were reportedly heard by his followers, then told to others who then told them to others who then wrote them down. But the various hadith differ widely among themselves, and many are believed by some Muslims but not by others. But even the most authoritative hadith is never strong enough to contradict the words of the Qur'an, all of which were reportedly given by Allah to the Prophet Muhammad and immediately written down under his direct supervision.
So what is the best outcome of the current situation, in which our shiny new Showcase of Democracy, Afghanistan, seems ready to convict and execute a citizen simply because he converted from Islam to Christianity? Are we happy that we worked so hard, with many deaths and much expense, to establish such a "Democracy" as this? Will we perhaps be so fortunate as to help establish another one just like it in Iraq? Is that why we are in Iraq, to promote Democracies such as this?
The only good outcome is for the Islamic courts, themselves, to consider all the evidence then come to the correct Islamic verdict, which is: "Case dismissed," because the Qur'an itself does not prohibit such conversions, but in fact permits them under the rule in Qur'an 2.256, as shown above.
If the government of Afghanistan merely yields to Western pressure in this one case, that doesn't solve anything. The problem will come back again in future cases. And if they make up some phony excuse for not having the trial, like "mental incompetence," that is even worse. The fact is that Abdul Rahman is perfectly competent to stand trial, but the case against him is not justified under true Islamic law.
PROPOSAL FOR SOLUTION, WITH BENEFIT FOR ALL
I propose that a high-level team of Islamic scholars study this case, and defend Rahman, and win the legal victory they deserve: "Case dismissed." This would establish the Islamic legal precedent, on the international level, that true Islam permits freedom of religion. This might very well be as important a case for the entire world today as Brown v Board of Education was for the United States in 1956. And it could be the foundation of true Christian-Muslim understanding and peaceful co-existence, as described below.
The world is well aware that a fundamental tension has long existed between Islam and Christianity, Muslims and Christians. The underlying theological reason for this tension is best understood by comparing two verses from Scripture: Sura (chapter) 112 from the Qur'an (Islam's highest written authority) and John 3:16 from the Bible (Christianity's highest written authority.) Sura 112 is considered by many Muslims to be the most important single statement in Islam, and John 3:16 is considered by many Christians to be the most important single statement in Christianity.
The fundamental conflict is that the Qur'an says Allah (God) did not father any children in any way, and that no one is like Him; but the Bible says that Jesus is God's Son and that anyone who believes in Jesus will have eternal life. Islam accepts Jesus, but only as one of the many prophets who came before Muhammed, not as the only-begotten Son of God.