I apologize in advance for how long this reply is.
I thought I'd allow for speculation in my summary, as I'd be interesting to see what people could interpret. At the top sits a totalitarian regime who have by improbable, but also incredibly lucky circumstance, found themselves upon a completely obedient society. They are the same organ as the one who sat on power when the Great Reversal came to an end, the leaders of Unified Europe. They remain in power because they are isolated from the population. The only information the population have about the government is from the messages they receive every few months, otherwise they are invisible and remote.
Hmm, would they be the business oligarchy who originally founded the technology to create the Substance? They would have the money to influence multiple governments and unify them where the EU couldn't, and create their own private police force to keep the people quiet (and might be how all those dissidents go missing?)
The average person, or rather, everybody, is left in the dark about the Reversal. They believe they are still working towards it. In reality, they have all become slaves, as the processing of this new substance is also turned out to be of unimaginable value.
I can see how a common goal could keep people quiet. 1984 had some great slogans to that effect, didn't it?
As I'd like to keep this somewhat believable, I am yet to settle on what it actually is. My first thought was the discovery of a new element, but I'd like to hear how scientifically probable that is before I decide. The reason human labor is required has several factors:
For over a hundred years, humanity allocated of it's time and resources to surviving the changing climate of Earth, in addition to finding a cure. Before it became noticeable, humanity was close to creating fully functional AIs, but all development was then halted. So, in the present, the technology for fully functional, trialed and tested robotic labor does not exist. The production of automated factories was not an option as the Cataclysm began, as the labor factories were mass produced in a hurry; being both cheaper and more reliable than automated ones. In the present, the government has no reason to replace humans with robots, as they have essentially created a perfect population by accident.
Great! So I'm guessing either society will have regressed in terms of technology or knowledge is artificially withheld by the government a la Brave New World? Both options could also explain why it's so easy to keep the population misinformed. What technology do they have left?
I have not read any of these books, so I cannot answer. I will definitely look into it, however!
Sorry, I just picked books that I've read!
The Quantum Thief is set on a planet where time is literally money--everyone has a watch that counts down to zero. You exchange units of time for everything, from basic necessities to extravagant luxuries. Once your time runs out, you carry out a sentence of hard labor (during which you're not even a slave--you're barely even sentient), to be reborn with a full watch once you're done. The society is egalitarian to the extreme--there are no differences between the genders, as there's no childbirth; no one is rich forever (since your clock is ticking down anyway) or poor forever (since your sentence will end). The big reveal is that SPOILER. The story explores the themes of happiness vs freedom and what they truly mean. It's also set in a really cool world (secret masked society! Clans that started out as MMORPG guilds! A cloud-based collective unconsciousness!), which makes it really fun to read.
The Giver is also set in an egalitarian world, where children are born in vitro and assigned to families, where every aspect of their life is monitored and dictated by a group of Elders. It's never explicitly stated in the book, but the Community is run like it is the only (last?) point of civilization in a post-apocalyptic world, which ties into your theme of survival vs complacency, as well as what happens to human nature when all differences are erased. I recommend the book, but please don't watch the movie first.
Anthem is a propoganda pamphlet pretending to be a story (Seriously, the Wiki article is 5000% better written). It doesn't pretend to be a utopian society like the other two books, but it hammers home the dichotomy between the individual and the collective. Ayn Rand argues that the natural state of humankind resides in the demands of the individual, and any attempt to put aside those needs for the greater good of society destroys the essence of humankind.
The three are very different books, but you can see the common springboard (a highly egalitarian society, ruled by a totalitarian and secretive elite, powered by the plug-and-play masses who are only too happy to swallow the lie) the authors use to launch their idea. It's the protagonists that are different, representing the three different ways you can approach the problem:
The outsider: The Quantum Thief is told through the eyes of someone who used to know the society, but erased it from his own brain. In essence, he's a foreigner, and b/c the natives don't really welcome outsiders, learns mostly through espionage and the occasional social faux pas. The book gives our climax when he's struck by a deus ex memory, but can be (should be!) done by good old sleuthing. This is basically a detective story, and works great with mystery conventions.
The convert: The Giver's protagonist used to be a true believer, until he met the eponymous Giver. He's given the memories the Community has chosen to repress, and in doing so, changes his entire worldview. Nothing in the society changes, but every memory changes how we view his world, often in horrifying ways. This is a coming of age story, and works best with all the tropes that come with it. I think both Divergence and the Hunger Game trilogies owe a lot to this book.
The black sheep/Messiah: Anthem's protagonist was born in the society the story is set in, but was different from day one. He fought against convention time and time again, until, driven out, he resolved to change it from the outside, from the ground up. Think of Neo in the Matrix, Sansa Stark of ASOIAF, just about every YA protagonist... I'm not a huge fan of this approach tbh, b/c it's really easy to end up with a Mary Sue/Gary Stu, but a lot of great stories owe their story arc to this trope.
Islam is a natural choice, as I want the setting to work historically. Statistics show that while ethnic European birth rates are in decline, birth rates of those with Asian or African descent are increasing, predicting a huge population rise in ethnicities from Muslim countries. Also, Islam is the fastest growing religion in the world, and this is particularly true in Europe, where the number of converts is also accelerating. Back to the fictional universe, religion tends to flourish and spread in times of crisis, and especially among the uneducated, which all of them are.
I agree that the unegalitarian philosophies in Islam might be contradictory. I wrote "modernized Islam", because I believe that sooner or later, Muslims in Europe need some kind of a reform in order to be compatible with modern values, so perhaps in this reformed version, there will be more compassion for women.
Atheism/Agnosticism is growing faster than Islam in Europe, but I agree that in the face of uncertainties, people find strength in religion. You're right--Islam might well be the dominant option by the time people start looking for a higher power.