Islam is also based on Abraham, Moses, and the other prophets of the Jews, and Jesus and the Apostle's as well. Everything you accuse Islam of equally applied to Christianized Europe. And not only was Europe like that, things like widespread literacy and domestic abuse laws are still fairly new concepts in Western culture thanks nearly two thousand years of Christian rule.
The problem is, while there is no mandate to convert, the Quran does instruct Muslims to kill infidels. According to the Quran I should be killed because I question and deny Allah. According to Christianity I should be killed for not wanting to Christ to reign over me. According to Judaism (well, not really, since they're the only ones who really don't give much of a crap about what others are doing and wouldn't claim their laws apply at all since I'm not Jewish - but Jesus made it clear these laws are still valid to his followers), I should be killed for not worshiping the god of my father, who is the same god of Abraham.
That's what happens when you follow the law of those books as they are written.
We have and are making better functioning societies. It's been a few hundred years since anyone in the West has been tried and executed as a witch. We are slowly granting more freedoms by booting religion out of the state. Today we can protest a state official. To do so when the Church ruled was to defy the very will of God himself, and was punished with horrible deaths from being slowly and brutally tortured. The Ottoman Caliphate was more sophisticated, and more intellectual than Christianized Europe by far, even fairly progressive for their time in allowing Christians and Jews to practice their religion and for the adoption of Greek philosophy, but they too had brutal cruelty, slavery, lack of women's rights, and to challenge the Sultan was to challenge the will of Allah.