Here are just a handful of verses from the Quran that peaceful Muslims say that ISIL and other violent Muslims routinely violate:
“There is no compulsion where the religion is concerned.” (Holy Quran: 2/ 256)
"Say to the disbelievers [that is, atheists, or polytheists, namely those who reject God] “To you, your beliefs, to me, mine” (109:1-6)
“If thou dost stretch thy hand against me to slay me, it is not for me to stretch my hand against thee to slay thee: for I do fear Allah” (Al-Ma’ida 5:28)
“Do not be people without minds of your own, saying that if others treat you well - you will treat them well, and that if they do wrong - you will do wrong. Instead, accustom yourselves to do good if people do good and not to do wrong if they do evil.” [Al-Tirmidhi #1325]
“Surely they that believe, and those of Jewry, and the Christians, and those Sabeaans, whoso believes in God and the Last Day, and works righteousness–their wage waits them with their Lord, and no fear shall be on them, neither shall they sorrow.” (5:69)
“The truth is from your Lord, so whoever wills - let him believe; and whoever wills - let him disbelieve.” (18:29)
“So if they remove themselves from you and do not fight you and offer you peace, then Allah has not made for you a cause [for fighting] against them.” (4:90)
“And serve God and do not set up anything with Him, and be kind to the parents, and the relatives, and the needy, and the neighbour who is of kin, and the neighbour next door, and the friend far away, and the traveller, and those who are still dependent. God does not like the arrogant, the boastful.” (4:36)
“The true servants of the Gracious One are those who walk upon the earth with humility and when they are addressed by the ignorant ones, their response is, Peace;” (25:63)
“He does not forbid you to deal kindly and justly with anyone who has not fought you on account of your faith or driven you out of your homes: God loves the just.”(60:8)
I reject any assertion that the interpretation of ISIL and other violent extremists is more valid, accurate, literal, or true to the Quran than the interpretation of peaceful Muslims. All religious texts can be interpreted in a way to support violence, and all can be interpreted in a way to support peace. The Quran is no different than the Bible in this respect. I believe that discrepancies in the statistics of violence and acceptance of violence are due to factors other than religious texts, just as they were in the periods of history in which the Muslim world was generally more peaceful and tolerant than the Christian world.
To be clear, I’m not saying a peaceful interpretation of the Quran (or the Bible, for that matter) is more true or valid than a violent interpretation. I’m just making the point that every reading requires interpretation, and that there are apparent contradictions in both texts, and in this sense there is no difference between them.