Integration is such an interesting term.
Before we got to see what the internet actually became, it was a realm of endless idealism. It was going to be something that would finally unite people across cultures and any sort of boundaries. People would be able to share ideas, communicate instantly, and effectively turn humanity from a disparate group of people separated by arbitrary lines into simple a group of diverse and interesting people all sharing and communicating among one another. Instead we used its filtering ability to break down into even smaller groups than before. Before the internet Americans were mostly unified by an American identity. Now instead we've splintered off into a whole host of little subculture identities driven by the great ability of the internet to unite niches and expel the nonbelievers.
But this isn't about the internet. It's about people. Birmingham is one of the most "integrated" cities in England. This [1] page has heat maps showing the various religions there. There's basically no overlap. Instead of integration you have the Muslim section, the Christian section, the Jew section, etc. Even the Sikhs have there own little section, though granted they do share it a bit with the Hindus. Now instead of having one mostly unified city you now have a half dozen cities that have some very sharp cultural conflicts. The irony that literally bringing people closer together can, figuratively, do the exact opposite.
Even the notion that we're becoming more integrated is something I'd question. This [2] is a video showing the borders of the world over time. The surprising thing you'll notice is that, over time, divisions between society have actually been accelerating. Check out the mid 1200s. The Mongols created a single unified empire than stretched from western europe to eastern asia. Very near the entire known world at the time. No need for borders when there's one world government, and one that was also extremely tolerant of foreign cultures. Can you imagine living in this time and then somebody saying that within a couple of centuries the entire empire would be scattered like ashes in the wind?
And like nearly all the empire collapses you can see in that video, it was caused by internal culture clashes. Should the Mongol empire adopt western traditions and become a sedentary settled empire, or should it remain a putative Mongol empire? One side said x, the other said y, lots of people died, the empire broke up. A story told a million times on various scales. Of course even if they had chosen one direction or another, it likely would have had the same ending because once one side or another reached a critical mass - you'd see the emergence of internal insurrections.
Of course we've had a pause in open war since 1945 but nuclear deterrence isn't going to last forever. Imagine there were no nuclear weapons today. Do you think China, the Mideast, the United States, China, Russia, Europe, etc would still be maintaining the already tenuous peace we have? Without nuclear weapons the Cold War would not have been the Cold War, it would have been World War 3. And as soon as nuclear deterrence can be nullified by technological means, I expect we'll be quite quick to pick right back up.
[1] - https://en.wikipedia.org/wiki/Religion_in_Birmingham
[2] - https://www.youtube.com/watch?v=-6Wu0Q7x5D0