We'd naturally fork, because that future sounds like a dystopic hellscape to many (if not the overwhelming majority).
And indeed once we reach the point of being able to reliably colonize other planets, large scale splintering (both physical and cultural) will begin near immediately. You'll have libertarian planet, Islamic planet, even the Mormons will finally have their planets! And so on.
And the people who want to sacrifice their bodies to go enter the machine will certainly have their own little slice of the universe as well.