Islam won't. It can't. It is an algorithm of hermetically sealed thought that has no foundation within it for synthesis or argument with itself. It enforces itself by death sentences. It's ideological base is fundamentally opposed to the value set we of the West depend on for democracy and our way of life. Islam, just like Communism, must be confronted head-on at its roots, and the message needs to be repeated over and over again.
Interesting. Christianity spent between 500 and 1,000 years in this kind of inflexible character. I believe the last religious-based death sentences in Europe took place less than 200 years ago. In post-Moorish Spain, it was not illegal to be Jewish or Muslim. The principal targets of the Inquisition were the large numbers of Conversos, and to relapse was punishable by death.

Many non-Christians find tenets of Christianity to be disturbing, particularly its powerful insistance on conversion, which has had the multiple effects of self-rightiousness, intolerance and the overwhelming of local cultures.

For 1,000 years, the most religiously, culturally tolerant empires were those that followed the Islamic conquests. Much of Western antiquity was preserved by these empires and rediscovered by Christian invaders during the Crusades, laying the foundations of the Western Renaissance.

To see Islam synthesized with the modern world, I recommend visiting Cairo, Istanbul, Sarajevo, Baku, Jakarta, even Tehran (where the current populist president was elected in opposition to the more moderate candidate preferred by the powerful religious elite).