Actually there are a number of mistakes in Bray’s commentary. I think that Mohammad’s main fight was against Jews and pagans. It was not until the crusades 3 or 4 centuries later that Christians became such a major enemy. There had been lesser clashes in Egypt against the Coptic Christians, successful; against Constantinople; against Spain; and against France, unsuccessful. The Arabs had been busy invading Persia, and fighting the internal battles that have resulted in Sunni and Shiite.
His efforts began in the 600’s, not the 700’s (8th Century). Under Mohammad’s laws only his wives were required to have full cover. His first wife was a successful business woman, and I strongly suspect left the house when she needed to. There are many Muslim laws on exactly how you should live, as are similar to Jewish laws. They both go into detail on what and how you can eat. For example cutting off the right hand of a thief is a more terrible punishment since it means you cannot eat from the communal pot or tray. The left had is used for body functions (good sense in a culture short of water), and the right hand is for eating. People following such rules of living and washing hands 5 times a day for prayer probably died a lot less from diseases. Thus Islam grew and survived. Christianity does not have this level of detail.
About the history of the spread of Islam, well, you may wish to take another look. You say the early fight was mostly against Jews and Pagans, and that’s true for a FEW years—in the Arabian Peninsula, but once the Islamic invaders reached Syria/Palestine and Egypt, well, almost all the inhabitants were Christians.
And the Egyptians were pretty much ALL Christian, Coptic or otherwise, and Islam conquered them; converting many, killing not a few, and dhimmituding the rest. I doubt many Christians in Egypt saw the struggle as a “lesser clash”. Same in Syria, Palestine and Babylonia. After Egypt, all of North Africa, once Christian, was forced into Islam.
Many people seem to forget just how Christian the Roman Empire and it’s remnants became toward the end of the Empire. This included ALL the Roman/Greek areas of the Middle East. Constantine made Christianity first an official religion of Rome around 310 AD, and then later, over the next two centuries, it became THE Religion of Rome. This happened at the end of the Roman Empire, but the spread was pretty much throughout the Empire until it fell; battered by invading gothic barbarians and a few centuries latter, invading Islamic hordes.