More words on the ending of Shin Sekai Yori and the show overall
(There are plenty of spoilers here.)
This is sort of a reaction to Bobduh's articulate review, where he covers both why the show is excellent and why despite this it leaves him cold. While I've come to sort of agree with him about some of its flaws, what elevates Shin Sekai Yori to greatness for me anyways is the power of its ending, specifically roughly the second half of the last episode, and how I read it. Rather than simply give us an action show resolution to the situation in the ruins of Tokyo and then a straightforward upbeat epilogue, Shin Sekai Yori instead went out of its way to give us an uncomfortable ending that grants humanity to previously inhuman characters and systematically strips away the idea that the Cantus humans are the clear heroes; even Saki, our sympathetic protagonist character, is revealed to still be reflexively prejudiced. If there is a hero of the ending it's shown to be someone viewers had probably been looking down on and hating. This is a dramatic and powerful reversal of the situation that leaves us without comfortable or easy answers (and the revelation in the final coda of the show drives that home).
To be specific, I think that the staging and presentation of the ending makes it clear that we're supposed to sympathize with Squealer, not the Cantus humans running the trial. The whole visual vocabulary of the trial is that of a humiliating show trial, Squealer engages our sympathies throughout with both logic and bravery, and what happens to him is horrible. The final revelation at the end of the show finishes this off by giving the viewer no refuge for prejudice and no grounds to look down on the queerrats. I am not at Bobduh's level of 'burn down the Cantus humans' but the ending makes me believe that we're supposed to feel uncomfortable about what happened with Squealer (and even that it was unjust), and I do. At the same time the show has spent the entire run building up Saki (and Satoru) as our viewpoint and people we like, so we didn't want to see them die either. This dilemma is where and why I think the show becomes great.
(In fact I think most people will have been reflexively rooting for Saki right through the action in the ruins of Tokyo. Only when the show pulls back afterwards to give Squealer's side of things do doubts start seeping into our minds. I'm pretty sure that this is deliberate on the show's part; it wants us to be caught up in Saki's viewpoint and then come to a skidding halt as things look more and more disturbing afterwards. Some people may pull themselves away beforehand but I didn't really.)
To me, where Shin Sekai Yori excels is in raising hard questions and then not giving us comfortable answers. As I wrote at the time everyone is doing horrible things because they are all trapped in horrible situations. Over and over the show gives us a clear evil to rage against and then shows us why that evil exists and how it is the result of well intentioned people doing the best that they can in a terrible situation. There are no morally bright characters that we can root for without qualms, not even Saki and Satoru at the end. For all that Squealer is not a nice person, even his rebellion is morally defensible, as he carefully explains to Saki (and us, the viewers). I could do worse here than quoting @llvn from Twitter:
I love how it presents complexity without judgment. Everyone is wrong. But they deserve life, freedom.
Shin Sekai Yori is both a picture of fallible people trapped in a terrible situation making the best life that they can, mistakes and all, and a show that confronts us with hard questions that it doesn't give us any comfortable answers to. It doesn't give us any heroes or any clear villains; instead it makes us uncomfortably understand all sorts of people who are doing terrible things.
(Similarly, what happened with the queerrats is extremely unpleasant but it's also pretty much the result of relentless logic. Also note that even Kiromaru, the 'good' queerrat, is a complex character with his own motivations that don't neatly align with those of the Cantus humans. After all, the entire reason Kiromaru came to the ruins of Tokyo the first time was to see if he could find some effective way to rebel.)
By the way, I would probably have a somewhat different reaction to the end of the show if I thought that the show was presenting the Cantus humans as being successful. My view is that it's rather to the contrary; the Cantus humans are on a not so slow decline due to a shrinking population base and repeated horrifying incidents such as what happened with Shun (cf the worldbuilding bits pointed out in this comment). Since I don't like the Cantus humans and think that the world would be better off if they didn't exist, this is okay with me.
(I'm pretty sure that the show also agrees with this position since I don't see any particular sign that the show considers its world of the future to be a better place than today.)
As for the flaws (or at least one ongoing flaw), I have to agree with Bobduh that in retrospect the protagonists are the weak point of Shin Sekai Yori. I don't want to sound too negative here because I don't think they're bad (I found them and their interactions perfectly believable), but they are pretty passive. Shin Sekai Yori is not a story about Saki acting forthrightly to change her world, it is mostly a story about her experiencing and coming to understand it. In that sense Bobduh is right; this is more a science fiction story about setting and ideas than a story about actual people.
Sidebar: an alternate reading of the show
To be fair, you can also read Shin Sekai Yori in a different way. I can construct a plausible reading where the Cantus humans are right to be as cruel and brutal as they are to everything and where the show is an argument from utilitarianism. In this version of the show, Saki's life is the story of a tragedy (and she even tells us this in a voiceover); her moments of rebellion against the proper way of the village lead first to the rise of Squealer and second to the tragedy of his rebellion.
(Squealer's life arguably revolves around his first encounter with Saki and her friends. That fateful meeting not only saved his life and his colony, it also may well have put him on the path to rebellion by showing him weak, fallible, and manipulable Cantus humans.)
My justification against this simple reading of the show is how it handled Squealer's trial, specifically how it doesn't show the Cantus humans in a good light. They are not people handing out justice, they are the masters punishing an uppity slave.