You can only substitute one political system for another. Similarly, you can only substitute one religious belief system for another.
It is relatively easier for a Government to promote a political system than to promote a religious belief system and that is the essential difference between engagement with the Soviets and engagement with Islam.
The battle against fundamentalist Islam cannot be won without the active participation of the Church.
(Sadly, the number of missionaries in key battlegrounds like Iraq and Afghanistan are very small and the security situation severely hampers US humanitarian efforts).
Our political system is based on a religious belief system.
The American notion of freedom is in place because Christianity made it so.
As we promote freedom (with the carrot of humanitarianism, missionary work, and business investment and the stick of military force...BOTH carrot and stick are representative of christian values BTW) the message is getting through.
We've made progress...and that will slowly continue. And that's because the Church IS doing it's job through politics and through other avenues.