There really is no such thing as a 'moderate Islamist'. Once you decide you will inflict your religion as interpreted by the government of the day on anyone and everyone, you are not moderate at all, you are a religious fascist. Of course they can scream 'god is great' all day long in a liberal democracy where individual ideas are supposed to be tolerated, encouraged and expressed over ideological group think. Conversely, try starting an atheist demonstration in a 'moderate Islamic' setting based on "god doesn't exist" or something similar and see how that goes.