But those small battles are used by the terrorists as recruitment tools for the big battles. The ban on the veil is often cited as a motivating factor in France is getting attacked. I'm afraid you can't just separate 'mainstream' and 'radical' Islam that easily. On the Venn diagram between the two, there is an alarming amount of intersection.
Sure, but we all have articles of faith, don't we? For us it's pretty much a mechanical article of faith to say that democracy is good, free speech is good, women and gays should have the same rights as straight men and that there should be no racial discrimination.
We take those things as givens, but they are anything but in global and historical terms. They are, in fact, simply products of our time, our society and moral outlook. Equally, the belief that there is no god but Allah and Mohammed is his messenger is just as much a given to a billion or so muslims worldwide. We may see it as madness, but it's nothing of the sort. It's just a different belief system.