I think the transposition is fair enough in terms of the possibility of the Bible being used to justify all sorts of heinous acts, even if you allow for some difference between the overall tone of the NT v the OT.
I would also say that there obviously individual Muslims that have no truck with any sort of violence and do have a live and let live attitude. The problem is that these seem to have very little voice.
It's not really about "not real Muslims/Christians" though. What is so difficult about the spiritual leaders of the Muslim people of Scotland and Glasgow being able to join with others in a visible act of condemnation? What is it about the general cultural that means individuals and leadership are not empowered to raise a voice for tolerance and anti-extremism.
Christianity has a torrid history when it comes to persecution, white elitism, violence and extremism. Thankfully this is (a) pretty much a thing of the past and (b) widely condemned when it does happen. Why?
Because most "Christians" couldn't care less what other people do so long as it does not hurt anyone else, regardless of what their interpretation of the Bible might have to say about it.