I think that's partially what's going on with the Cordoba House controversy. Islamophobes in America don't even want to acknowledge the existence of Islamic moderates like the ones running the Cordoba project, so they lump all forms of Islam together. And to the extent Islamophobes succeed in killing or tarnishing the project, they succeed in harming moderate Islam. That's just great for extremists in Islam, or even unreformed and undemocratic elements of Islam, and their behavior will then just reinforce the power of Islamophobes.
What to do about this symbiosis is less clear, except that the cycle can work in reverse, of increasing moderation. I think the Cordoba House will be built and will help increase the influence of moderate Islamic leaders at the detriment of Islamic extremists and American Islamophobes.
I've also thought the Cordoba House could highlight the Muslim victims and heroes of 911, something that could help blunt the claim that the project is somehow an affront to the memory of 911.