All very interesting, but it then begs the question: the Byzantine Christians did not want to become Muslims. They were worshipping God in the Christian way, and many were quite devout.
The Muslims invaded, thinking the way they do, and the victory went, in province after province, to the Muslims. There were a million different instances of chance and good fortune that could have cut either way, but God chose to let the Muslims win. One example of this, in a slightly later period: on the Third Crusade, a truly enormous Western Army was descending on Outremer to assist it in beating off Saladin. The Christian army was in three parts, with the largest part being the army of Fredrick Barbarossa, Emperor of Germany. With that Army, the Crusaders were virtually guaranteed a victory, and thereby would have restored most of the Middle East to Christendom, and preserved Christianity.
But Barbarossa had a freak accident crossing a river in Asia Minor, and drowned. This was not a matter of act of free will; it was an act of God...an act of God that caused the Imperial Army to melt away and abandon the cause. Coeur de Lion and Philippe Auguste were both still able to reduce Acre and to hold their own against Saladin, but there was no prospect of breaking Saladin and Muslim power after that. Now, I look at that and I see a divine choice, an act of God that determined the outcome of the Third Crusade, and thereby doomed Christianity in most of the Levant.
And I wonder, theologically, why God let the Muslims utterly triumph over the Christians.
The Christians weren't just defeated, but the Christian religion and way of worship was permanently deleted from those lands.
The concept of free will is an all or nothing concept. If you believe in free will, whether or not you are devout will have nothing to do with whether or not you will win a battle. It's on you.
The free will to conduct yourself properly while on earth has nothing to do heavenly intervention.
If free will is absolute, then there is never heavenly intervention. But the Bible indicates that, at least on occassion, there is intervention, which implies that free will may not be absolute.
But it is also a false premise to assume that heavenly intervention and free will must be connected in any way.
In order to make choices on good or evil, one must know the difference. Perhaps God let Islam spread for just that reason. Perhaps there needs to be a balance. To choose, one must have choices. To choose properly, one must understand the nature of the choices.
That is one of the problems with many people today, especially with regard to the war on terror. They have had it too good for too long. They are unable to understand evil. Some people have to experience a thing before they understand it.
Why did God let 3,000 people die on 9/11? Perhaps God lets us do what we want to each other in hopes that some of us will "get it" before the end comes. If he intervenes from time to time, it may be only to bring things into balance before things get too far out of whack.
Who knows? I don't. None of us do. All we can do is stand against evil where we can, promote good to the best of our ability, and hope it all works out in the end.