In an essay examining The Kindly Ones in the context of other Holocaust literature, Garth Risk Hallberg nails the reason why this book is so polarizing:
But it is Littell who, by writing a 975-page novel from the point-of-view of a sexually damaged S.S. officer, has invited the burdens he must now carry. His work can achieve its totalizing ambitions only to the extent that it exhausts every facet of its monstrous subject. That Littell manages to embody so completely the difficulties of finding a new literary approach to his subject thus testifies, perversely, to some degree of success. For The Kindly Ones, which seeks to drag readers through the heart of historical darkness, does us at least this kindness: it brings us valuable news about the way we live now.
Garth doesn't explicitly connect the dots, but I think it's implicit in his piece: we understand certain ways to discuss the Holocaust, The Kindly Ones offers a very, very different method. This inflames feelings.
Interestingly, Garth seems to view The Kindly Ones as a failure not in approach but in delivery. By all means, drag the Holocaust down to the level of the everyday, but replace it with something else that's sacred:
Such is our current situation. We've moved from the Eichmann in Jerusalem controversy to the Angel at the Fence kerfuffle, from The Drowned and the Saved to BOY IN PJS. We've crossed the great divide between reverence and "meh." This movement is called postmodernism, and in abler hands than Littell's, it may yet prove itself capable of finding new ways to speak about the unspeakable. And yet it's worth remembering that its direct forerunner, Friedrich Nietzsche, called not for the abandonment of all values, but their revaluation. The example of The Kindly Ones suggests that that revaluation becomes more difficult, not less, in the absence of something to rebel against. When nothing is sacred, there can be no sacrilege.
I'm not so sure I'd agree with all of this. True, not even the Holocaust can resist cheap commodification, but I think the fact that the depiction of the Holocaust in art can still so easily raise a controversy does say something for our reverence of it. And as the last presidential Administration demonstrated, there's still a fairly large fraction of America (not to mention the postmodern world, however you define it) that can get worked up over sacrilege. That isn't to say that the world isn't a little more like Garth says it is than it used to be, just not so much as Garth seems to be saying.