"
Why did people in the Middle East gradually convert from Greek and Coptic Christianity to Islam? It made their lives much easier, they had better legal rights and paid lower taxes."

That is a nice point of view, but, unfortunately, quite remote from reality.
If you were not a Muslim you were part of the sub-humans categories if you belonged to the Religions from the Book (Jews and Christians) and none-humans if you were a Pagan.
The second one was promptly executed.
The first category was permanent slave, had to pay for life every year, and no legal right whatsoever, had a status of dhimmis. Their children could be taken as slaves for whatever purpose for sexual use to military use.
So the reason why they convert was to save their lives, get legal rights and pay taxes only in money, having access to proper job, having the right to own properties (and not being one). Roughly.
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