I'm not sure of the context but they were allowed to live as you put it. They were prohibited from any influence on government. They extracted taxes from religious minorities and they didn't have a place to go anyway. After the end of the ottoman empire millions of christians migrated to the west, especially Brazil, where we now have more lebanese than lebanon itself.
That was mostly a compromised the muslims reached because when they conquered these lands they were mostly christians and it made no sense to kill or expel everybody. Pogroms against christians and jews were common though. And foreign christians were not allowed to move to islamic lands, that's one of the reasons the portuguese were so eager to find a route through the Cape to reach India.
The french colonized Lebanon and made it a christian country too, but after the civil war christians lost their power and they're slowly disappearing.
Muslims never had secular presidents in the sense we understand in the west. They had secular dictators supported either by the west or by the USSR that called themselves presidents. Like Saddam Hussein. As soon as they were toppled they elected religious leaders. There is one exception, Tunisia.
Western Christians treated Jews similarly. They were allowed to live in ghettos.
Still better than the super tolerant christians. I can think of maybe 1 or 2 Christian country that has a sizeable muslim minority that didn't come in just recently. (unless you use most of the war room standard which is more than 0 muslims is too much)
Regarding the pogroms, they were a common sight in Europe even after the enlightenment. When people their religion seriously, they do these stupid things. Western society as a whole has embraced secularism and managed to outlaw or discourage extreme forms of christian worship.
and Portugal was looking for a different route because it was tired of the Ottoman Empire controlling trade with Asia through the Mediterranean Sea. Has nothing to do with Portuguese people wanting to move to the Middle East.
The situation with Lebanon isn't that simple. The muslims and christians there lived in an uneasy peace but all of it changed when Israel was created and it drove Palestinians out and a lot of them came to Lebanon. You can see how a mass vengeful, embarrassed, religious crazies can upset such a delicate balance. Note I'm not saying Israel is right or wrong, thats a different discussion. I'm only talking about the effect of it on Lebanon.
Gamal Abdel Nasser the second president of egypt was popular with the people and while he may have authoritarian, he wasnt some dictator like Sadam. He also had no western support since he stood against the British and was hated by them.
Egypt actually made an effort to combat religious influence in government and I applaud that. They have a lot of work to do though, especially in its treatment of Copts and civil society being more islam centric.
mohammed mosadegh was elected in Iran and was secular. But you're right he wasnt a president, he was a prime minister and the U.S and Britain deposed him before he could really do anything.