If there was no Islam we would n't have the problem with groups like Al-Qaeda, but then again, we wouldn't have as much scientific knowledge
Why shouldn't the peoples inhabiting the Levant, Syria and Asia Minor not preserve and improve the heritage of Greek and Roman philosophy? Of course its flourishing is not completely independent from Islam. But the most significant factors for Arab progress was access to a large and wealthy community of Muslim peoples, and the mentioned ancient legacy.
For instance, I think a free and wealthy Persia is in very good shape to foster knowledge almost as much as Arabs have done IOTL.
Europe's setback wasn't due to Christianity, but to the fact that it consisted to a relatively large degree in only recently "civilized" and infrasctructured nations. Moreover, it was handicapped in climatic terms (in a Medieval setting), as well as cut off from India and other regions Arabs gained a lot of wealth and knowledge from.
You should also take into account that philosophical and scientific progress slowed down and finally stagnated in the Muslim world over time. Obviously Islam created a social atmosphere which encouraged preserving, spreading, and applying special knowledge, but not so much its expansion.
The Bible was not written down before the collpase of the Roman Empire I believe.
Duh, you ought to know that "the Bible" is not one book like the Qur'an is.
The New Testament consists of writings some of which were written as early as 40 AD, while others only cannot come from much earlier than 120 AD.
It is the 4th century which has the first collections similar to the eventual New Testament.
But how does that affect our topic here?