I'm not sure quite what future conflicts over religion in the world will look like, but one thing seems clear enough; the era of struggles between different world religions as they are traditionally understood is coming to an end. What we will get in its place are struggles between interfaith coalitions consisting of hierarchical, patriarchal fundamentalists and egalitarian progressives.
I got the impetus for this train of thought from reading James Loewen's "Lies my Teacher Told Me." Loewen mentions that American history textbooks rarely emphasize the role religious conviction has played in the lives of historical figures because of the objections of both religious fundamentalists, who will object to any unflattering portrayal of their religion, and axe-grinding atheists, who will object to any positive mention of sincerely-held beliefs. The latter note is extraneous for the moment. The interesting corrollary is how many formerly combative sects have come together to scrub any mention of their historical conflicts from the record. This is part of a larger compact between Protestants and Catholics, and between Christians in general and conservative Jews, which has been made in the past few decades, a trend which I think will continue into the future as more and more fundamentalists realize that shared material and power interest outweigh their theological differences.
Now, Ditchkins*-flavored Nu Atheists will doubtless jump in here to say that it is their gains and not the liberal religious which has caused the global circling of the wagons. This I doubt. Nu Atheists have a symbiotic relationship with the fundamentalists in which each replenishes the other's raison d'etre. They share, in the apostate class, a common enemy. And why would the Nus want to get rid of their most valuable resource; easily-manipulable strawmen? Plus, there is the reality that Nu Atheism in its design can never become a mass global movement; it exists to make Western liberals feel smugly superior from the ignorant masses, not achieve any kind of social change to threaten the entrenched power structures.
The greater threat here, as it always has been, is the apprehension by the religious elite that their own theological impulses can be turned against them. This has been most readily apparent in the past few decades with the Vatican's war on liberation theology and its association with the Latin American left movements. More recently (and more ambiguously) it has been the struggle between old-line evangelical Christians and the younger "emerging" movement which is dangerously apostate on the Real Issues. I suspect there were similar sorts of ecumenical kumbaya moments at comparable points in history; just before the Civil War, for example.
The other point of note here is that Western fundamentalists do at least still claim to be in conflict with fundamentalist Muslims. But this too seems to be more as a result of ongoing political necessity than any material disagreement. One would imagine that, when all sides come to realize their shared interest in censorship, patriarchy, and preserving the proper political succession, any alleged differences will also melt away.
*h/t Terry Eagleton