You're calling for an organic shift in ethics, laws, concepts of morality and judgement, perception and many other facets in a religion deeply rooted in ancient tradition with no measurable signs of coherent progress save for common regime changes. Now, Islam itself appears to be a peaceful enough religion, but a few have twisted it into something despicable and horrible to behold, through acts of terror and other absurd acts. It just so happens that those few happen to maintain a high profile, and are thus exposed to the world at large, and stereotypes and generalizations are formed. I personally have met only kind and hospitable Muslims, but that sample size does not tell the tale for all.
Same goes for people that claim to be Christians but shyt on other cultures and religions and tell non-believers their future spot is guaranteed in hell for eternity. I can't stand that greater than thou shyt.
In a nutshell.. Yes, it can happen organically. But a drastic event must occur, or a charismatic leader with modern and progressive teachings must come forth. Otherwise the world will simply continue to see nothing but this:
P.S. white people aren't helping.