Thank you for writing this insightful post. I know from personal experience that most in Bible-believing churches have a somewhat warped belief of Islam. Islam has changed greatly from what Mohammed first proclaimed it to be. It is more diluted but the methods of practice are still in place that are more worshipful than many church practices in America. It seems reminiscent of the temple practices, even.
To say that the suppression of women is, when it is actuated, the greatest fault in islam would be to ignore the GREATEST problem, and the treatment of women as individuals in any given religion supports that the greatest problem is the disagreement over Jesus's identity. Was Jesus a great teacher? Yes, he was... and religions all over the world tap into his teachings. Was Jesus a great prophet? Yes, he was... and His prophecy will never be undone. Was Jesus a man? Yes... all man, but He was also all God. What religions all over the world fail to digest is that Jesus was Prophet, Priest, AND King... God in the flesh for so long as He needed to live on this earth and fulfill the prophecies delineated in the Old Testament.
Islam does not agree that Jesus was God, but a good man and a prophet. But would a man truly good proclaim himself God? Jesus did and was nearly stoned by his people for it. If one has to refute His teachings on this point they have to refute them all... including His encouragement that we love one another. Jesus also died for those He loves and chose to save. Did Mohammed or Allah die to save those that love them and lay claim to their "promises"? Since a good part of Mohammed's teaching was that Jesus was a great man, and Jesus did something that directly conflicts with Islam, is not Mohammed, therefore, wrong in his teachings as well? And if Mohammed was wrong about Jesus, how can one trust all of his other teachings? Though many great things can be learned from Islamic dedication, one cannot say that Islam is anything greater than a method to live by for those that want to be good people... something that can be said about parts of most religions across this world.