24th of June 2037, barely 25 years since now. I do not know the reason for your optimism but I feel that there will be very little change in Muslim world in such a short time. This would be possible only if a strong liberal movement would be existing in the Muslim world, which is not there.
I always say that Muslim religion is difficult to live in and even more difficult to leave. The Quran prescribes death penalty for a muslim deserter. Despite this, there are more muslim atheists than we notice. Every society has closeted atheists who face difficulties in coming out in open and Islam is no exception.