The Egyptians were actually African not "christian", however after the Islamic conquest Arabia began exporting massive numbers of people, Arab people.
The Coptic point is only partially true, there was a coptic church in Egypt was one of the oldest around(churches in Arabia stretched right back to Jesus himself, as did the coptics) but the great majority of Christians in egypt were under the rule of byzantine lineage where the Coptics were unto themselves.
Quite right the majority of the Islamic world is not Arab, the Majority of the Arab world is however Muslim and all Arabs are..Arab.
I wouldn'y jump to the Bin Laden, Umayyid comparison either.
Bin Laden is attacking a western world which has bestowed a great many liberties and freedoms upon its citizens.
However the Umayyid conquest of North Africa and Andalusia (Modern Spain) was against a much less benevolent empire.
The Muslim political system bestowed more rights on Christians and Jews than they had ever had under Byzantine rule, charged lower taxes and tributes and protected the indigenous population much more than the previous rulers have. Contemporary sources at the time will verify that the majority of Egyptians were welcoming of the Muslim Caliph in place of any previous empire as with Spain. Do I deny that there were exceptions? Of course not, I would be glad to point you to examples of Big bad Muslim conquerors as well, but you'll find the population of North Africa and Andalusia were warm towards the Caliph (While most Arabia at the time actually wasn't, which is partly why they left Syria.
In Spain it was a very similar situation to North Africa.
IE The indigenous population found themselves under better rule than they had under the previous empire (though it would pale in comparison to todays standards yes yes yes)
But you're right about the assumption that the majority of the Islamic world is Arab when it is in fact a majority south-east Asian.
But Arabs are traditionally quite divided and are often too hot headed to see themselves as brothers, Islam went along way to improve and unite that, but it still exists very much today. Combine this tribal family first attitude with ideas of nationalism and war, you find the present situation can be traced back to pre-Islamic Arabia.