Put it another way, most "moderate" Muslims don't care, and in many ways they shouldn't. An extremist Islamist considers himself first and foremost a Muslim; it is his life's duty to do whatever it takes for the Cause. A moderate Muslim doesn't go around his daily life keeping in mind his religion all the time. He doesn't necessarily actively go out and search for Islamic organizations he can join, participate, and spew out rhetoric on.

The disproportionate voice is the result.

I do agree with you however that there is indeed a problem with these organizations "improperly" interfering with the lives of the people they're supposed to represent, and get away with it. I wish the governments would do a better job of preventing these kinds of repression from happening, though they usually either "placate" the wrong people the wrong way or pursue repressive populist measures that discriminate unnecessarily all the time.

Moreover, another angle of this antagonism can be seen in another thread around here, that one where the OP poster talked about his experience with the prejudices of his family. One finds a surprisingly high number of examples of ordinary "Westerners" who hold prejudices against Middle Easterners. I'd not be surprised if that provokes a kind of response from the "Muslims."