Mohammed
From my sense of history, the biggest conversion of Islam occurred in the second or third caliphate. Umar? Uthman?, I can't remember. Anyways the caliph decreed that Muslims do not have to pay tax because only Muslims were allowed to serve in the army. The tax burden would fall on the non-Muslims in this new Empire.
So many Jews, Christians, and idolators converted to Islam to avoid paying tax. I have to question their loyalty to their former religion.
The Ummyad treasury went dry, and the tax law was reversed in 3-4 years. But then, the converts were comfortable in their new faith. It was now cool to be Muslim because there were so many more of them.
And my sense of history is that the Muslims were not so kind to people "outside the book." Forced conversions occurred in Iran, almost wiping out the Zoroastarian religion. There were massacres of Hindus until that population submitted to Muslim rule.
If a person wanted to get ahead in this new empire, it was better to be a Muslim. Not exactly a forced conversion, but we could call it culturally induced.
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The same logic about justice could be applied to "Christian" nations invading Muslim nations to apply justice and elevate their people. Oh, wait! That has been happening for a couple of centuries. The Muslims don't like it.
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Again, today's examples of a wiser, kinder society are not there in the Muslim world. It is your job to fix that problem, not mine.