You kinda have a point there, except it was not Christians in a pure since, pure in a sense of doing what Christ had suggested "if you love me you will keep my commandments." There was no violence taught.
Some Muslims - many Muslims - would say that the violent jihadists, in most cases, do not represent them, and do not represent what they see as Islam. Same diff.
However, what some call the "Church" was the Roman Catholics who did do great harm, including killig Christians.
c'mon, the Roman church was the church. I say this as one who was once a bob jones, john r rice, sword-of-the-lord independent fundamentalist baptist, having cut my teeth on Chick tracts.
Anyhow... obsessively focusing on jihadists and extremists, and making that represent all of Islam, is disingenuous. It is comforting, easy to digest for the simple-minded and those seeking black/white world where they're the Good Guys and The Others are the enemy... but it isn't really true. IMHO, of course.