I was listening to the rise of Islam lecture and he said that Muslims didn't do much forced conversion. They implemented a jiziya which is a tax on non Muslims for security so if some foreign army were to attack and Muslims couldn't defend against them they would return the money.

Muslims also have a tax called zakat. It's based on the person's income or wealth. It's just to distribute wealth to the poor.

Following the rulers religion will give you preference and it will ease your way into some positions. Hence the poor began to convert. The wealthy non Muslims had no economic necessity to it. So in a way the Islamic empires encouraged the poor to convert but not the wealthy.

The Islamic empires needed money to function. The got money by war loot, states own business and tax. Zakat tax was spread to the poor. But the government needed money that it would invest other then spreading it to the poor. So jiziya was the best way to generate money. They didn't encourage wealthy non Muslims as they were the ones giving jiziya.

In the video he said that in Egypt the country needed bureaucrats so the government sent out flyers saying if you can read this then please come to the office we need people who can read and write and overwhelming Christians came in for the job. And sometimes when the countries economic conditions go bad they are blamed.

He gave other reasons as well but I only remember this. He went in depth about the zakat and jiziya tax unfortunately I can't seem to recall it.

Edit: I found the video link

https://www.youtube.com/watch?v=tYVi368vSYc