It took us 45 years, but we beat the Soviets without going to war. Way back when we all worried about the Cold War turning hot. Remember On the Beach? or Canticle for Liebowitz, or Seven Days in May? or "We will bury you" ? Amazingly, the fear of nuclear war on both sides restrained the military option, and the Cold War was fought out with propaganda, diplomacy, intelligence, and other non-lethal methods.
George Orwell got in the first solid hit with Animal Farm, and followed that up with 1984. Nobody could believe in the benevolence of communism after reading Orwell. Remember the Soviet spies Klaus Fuchs, the Rosenbergs, Kim Philby, Guy Burgess, and John Cairncross? They (and a bunch of others) spied for the Soviets, even passed the secrets of the atomic bomb to Stalin. By all accounts, these guys, all university graduates, were ideologically convinced that communism was the wave of the future, and they were doing good by spying for the Soviets. After Orwell, nobody worked for the Soviets out of pure love of communism. The later spies were all working for money.
Levi Strauss got in the second solid hit with blue jeans. Popularized by Hollywood westerns, worn by American teenagers, they became ultra cool behind the Iron Curtain, and Soviet teenagers would go to extra ordinary lengths to get their hands on a pair. It was hard for the commissars to work up much antipathy toward the Americans when every young Russian wanted to dress like the Americans did.
Detroit did some good with hot cars like the Chevy 409, the 'Stang, the 426 Dodge, the 'Vette, the Pontiac GTO, The Judge, and the whole drag racing, Thunder Road, and NASCAR racing scene. Again, hard to get young Russians worked up against the Yankees, when every one of them wanted to get their hands on Detroit iron.
Pop music, Elvis, the Beatles, the Grateful Dead, and all the rest of 'em ruled. Along with Hollywood movies. Again, hard to stir up trouble when every one in Russia is listening to Western pop music. We need to resurrect both pop music and Hollywood, and make sure they are getting into ISIS land.
In short we took down the Soviets with coolness, consumer products, popular music and movies. Plus a few other things.
This ought to be our strategy for taking out Islamic extremism. It worked on the communists, it will work on the Islamic crazies.