I find a great deal to admire in Islam. However, it seems to be essential to Islam that it aspire to be implemented from the top down through government, and that makes it very difficult for Muslims to buy in on the idea that they ought voluntarily to refrain from using government to pursue their goals, if it is indeed possible.
Remember how Islam was founded. Muhammad had been exiled from Mecca, then conquered by force of arms. The Qu'ran is written as a law-book. The idea of separating religion from state does violence to essence of Islam.
How was Christianity founded? Well, if was founded by people who didn't have political power, so the New Testament provides almost nothing about government except "render unto Caesar the things that are Caesar's." Now after Constantine, Christians did assume political power, and they did use political power to advance the cause of their religion. So, yes, Christians had the Crusades, the attacks on the Albigensians, the Spanish Inquisition, the Wars of Religion, and the Salem Witch trials. But after the Wars of Religion and the damage that these things did, Christian leaders started to back away from wanting to implementing their religion through government, and there is nothing in this that contradicts the essence of Christianity. Most of the people responsible for getting church and state separated were Christians, not secularists.
Yes, you can be violent on behalf of Christianity. You can also suppress religion violently. But there is nothing in Christianity that requires you to use violence to uphold Christianity, anymore than there is anything in atheism that requires atheists to use the state to suppress theism.
The "religion leads to violence" idea is based on a profound confusion. ANYTHING can lead to violence. But the idea that non-religious people have "nothing to kill or die for" while religious people do have something to kill or die for, is absurd. Some atheists believe that the progress of civilization depends on whether we "outgrow" religion or not. Why would people who believe that eschew the use of force to accomplish so important a goal, if the opportunity presented itself. OK, it doesn't involve anyone's eternal destiny, but the progress or regression of civilization? Important enough, for at least some, to use ridicule and peer pressure on its behalf.