How can this ever happen if they are never given the room to do so?

Oh what apologetic silliness. Want to compare the history of Western imperialism in the Middle East to that in Lating America? At best it's a draw. There is, after all, a reason why it's called "Latin America." But I'm not just comparing the Crusaders to the Conquistadors; this is all plenty modern; compare the Taliban to the Sandinistas, if you like. Or to any of the other numerous acts of military and political sabotage which Western governments in general and the American government in particular have visited upon that part of the world.

Why, then, do we not have a major problem with terrorists from South America attacking Western targets in impotent expression of their disenfranchisement? Could it perhaps be because 90% of people in South America are Christian? Could it be because mainstream Christianity does not teach that Biblical law should be implemented across the world by violent conquest? And why is it that those 350-some-million Christians in South America don't, to any significant extent, espouse the belief that -- as Leviticus instructs, for example -- gay people should be stoned to death, as massive numbers of "moderate" Muslims believe should be done to apostates in accordance with Sharia?

No. No no and no.

There is plenty to criticize about Western foreign policies. That criticism is entirely aside from the unequivocal statement that Islam as it exists today is the world's worst religion.