Right, stick to the tropes
You've correctly identified that any modern story must stick to the tropes.
Evil corporate-fascist state is a great start. Everyone from their Disney cartoons to their video games to their college education gets shoveled fed nothing but images of evil corporations. If Disney and Chomsky both say Stalin's interpretation of Fascism is the right one who are we to argue. (I mean who knows what happened to Dr. Junker or Carl Thyssen?) Not a single popular entertainment or education depict corporations as anything but evil. Break that trope and you get filed over next to Ann Rand.
So, your off to a good start.
But religion is very, very tricky. The only people allowed to be religious are people from primitive cultures, someone whom the reader will never regard as an intellectual equal. In modern popular culture, African-Americans are allowed to be religious for the same reason.
All religious people in industrial culture, especially white Christians, must be portrayed as viscous, bigoted irrational, selfish and never right about anything and never been. You can't mention their hostility to Eugenics, Freudian psychology or any of the dozens of other intellectual failures of the secular over the last century. You can't show religious people being far more generous and self-sacrficing and less violent than the non-religious population, no matter what the social research shows.
To make an acceptable religion, it must be non-traditional, having no history and thus innocent as new born babe. It needs to focus on the happiness of the individual but not require any sacrifice, obligation or self-restraint on the parts of the adherent. The religion is all about making the adherent feel good about themselves.
I'd suggest basing it on one of the hollywood religious fads. Maybe Hollywood Buddhism (no vows of poverty, no requirements of charity like traditional Buddhism) combined with some kind of matriarchal clergy. One must play up to female chauvinism after all.
The real key, as I cover under Chaos below, is that the religion cannot restrain sexuality in any form or to any degree. You can't suggest that obligations to the religion, society or children requires sexual self restraint. Otherwise, you’re a redneck bible thumper aching to set someone on fire.
As a crowing touch, make them the real nature worshipers, who worship a biosphere most of them have never seen.
That should make the religion acceptable to the target audience.
Now for shades of grey.
The best way to make a shades of grey story is to get inside the delusional world view of the "bad" guys and show how they sincerely believe they are doing the right thing. Look at the Nazis, the Imperial Japanese and the Communist. Most of the people who fought so hard for all three regimes where not bad people. Quite the opposite, they were people who cared and loved deeply, people who believed in making a better world for those they cared about.
Hate doesn't make a man a monster, love does. Hate fades, the sociopath will not sacrifice himself. To make a monster, find a loving man and threaten what he loves. He will come for you, unwavering and uncaring for his own fate.
That was Hitler's secret. People tend to concentrate on his hate mongering but that's not what made him effective. Instead, he created an elaborate fantasy narrative in which the German people as both a "race" and a culture, were under threat of genocide from a World Historical Conspiracy on the part of the Jews. Threaded all through the fantasy was a lot of truth but connected or bent to make them lies. German got unjustly blamed for the war, true. The Treaty of Versailles was unjust and harsh, true. Communist inside German were trying to cause it to collapse either so it would adopt communism or be unable to defend itself from Soviet invasion, true. A disproportionate number of Jews were communist, true. The Jews had created Communism and American free-market capitalism to destroy the German people, false. Americas commerce centered culture, its popular culture and pacifistic leanings were Jewish tools for destroying Germany, false. Stalin was planning on attacking into Europe, true.
A lot of people became fanatical Nazis because they believed that the German people faced genocide and had to fight their way out of "encirclement" seize the resources of the Soviet lands, knock out Communism and ship off the Jews to somewhere, or everything and everyone they loved would be destroyed.
Communist believed they were murdering for a utopia, a utopia so grand and inevitable that it as sin not to kill for it.
If you want to make a future totalitarian state that sounds plausible up front, I'd suggest one based on environmentalism. Since everything every individual on earth does affects the environment in some negative fashion, environmentalism give the pretext to regulate absolutely everything that anyone does. Even worse, environmental damage might actual require a great deal of control. (If Communism hadn't been a real threat then Fascism would have never got off the ground. Anyone who questioned fascism, got accused of being soft on Communism.)
But no matter how pure the goals at first, centralized power always corrupts.
The corporate-fascist state could arise because the government has to force people to use expensive and less effective technologies in order to protect the environment. That would devolve to the government dictating which technologies could be sold and thus what corporations prospered and which failed. Business success would not be about economic or technological creativity and testing in the market, but about government connections. The entire economy becomes a military-industrial-congressional complex. (it worked for General Electric big time.)
Any one who raised accusations of corruption, would be accused of not caring about the environment. (Wrapping in the flag.)
To further protect both the environment and the government allied corporations, the state will suppress all new technology under the doctrine of "precautionary principle" all technological change is assume to be more of a threat than a benefit. Of course, the definition of threat and safe will be done by state which will only allow those technologies whose sale will benefit the allied corporations.
Because of stagnated technology, resource creation stalls and they must use the resources that the frozen technology used. Instead of replacing metal with graphemes, ceramics etc they found space colonies to bring in metals that the forzen technology can use. (Space refining and perhaps manufacturing might solve energy and environmental problems as well.)
So, you have a "green" tyranny that looks perfectly fine to a lot of people these days. If it had a gloss of democracy and disguised the symbiotic relationship between government leaders and the allied corporation as regulation and high taxes, then it would look very plausible to most modern readers.
Behind the scenes things could get even more ugly with mass killing to eliminate "individuals excessive to the environments carrying load" and murdered by others who believe they absolute must do so to protect the environment and thus the future of the human race.
Nobody would know because everyone on earth would be so immersed in the ruling narrative that they regard as heresy any questing of the current political order as the same a being hostile to the environment, a green versions of wrapping one's self in the flag. People would be indoctrinated to only accept news from certain specific sources. Enough doublethink and you don't need active censorship
Meanwhile on in the outer colonies.
In the real-world, workers sent out into dangerous and isolated environments are well trained, well paid and have their grievances quickly addressed. That's because one pissed off, untrained, exhausted or sick worker can cause millions of dollars in damage. Not to mention the cost in capital that it cost to get them and their gear out there.
But that's not the trope so we forget that. That would make corporations economically rational which isn't allowed. Instead, the corporation must act like communist, sending workers out into the space gulags.
The workers, mostly political prisoners, will be shot into space with little care how many of them survive as long as enough do to get the archaic resources back to earth. (ignore how easy sabotage would be in space. Perhaps sending their families along as hostage to maintaining the facilities would work as would separating food production into other facilities.)
But desperation causes them to develop new technologies, possibly biological so they can disguise it from the earth authorities.
The war would come when a failing out among thieves happens between the various alliance between specific political leaders and their allied corporations. Formally, insiders would find themselves pushed out and failing.
At that point, they begin to turn to the outer colonies technology to try and prop themselves up. All evilly of course, they won't trade for it, pay for it, they'll steal, kidnap and torture to get it.
The outside corporation-politicians begin to gain, not more power, but more possible military power. A kind of war of economic sabotage breaks out (can't actually fight would destroy the environment, although killing people inside cities is probably okay.) The insiders then decide that the way to end the problem is to cut off the technology at the source and attacks the outer colonies either to destroy them or to place them under harsh and close supervision.
That's when all hell breaks loose. The earth regime has the overt power, the spaceships, the millions of military personnel, and billions of potential brains to turn to solving problems. Plus, they have a stable ecosystem to fall back on. The outer colonies have to devote a lot of time and energy just getting air, food and water. But earth technology is stagnate and they've likely forgot how to innovate. Their internal divisions make the hostile to anyone who does innovate.
Earth propaganda depicts the outer colonies as both starving earth of desperately needed "natural resources" while at the same time flooding earth with dangerous technologies sure to destroy the environment. Believing they sally forth to protect the economy and lives of earth's human population while protecting the environment from sinister unknown technologies, Earth's military head out with the belief that the desperation of the situation justify any ruthless extremity.
Meanwhile, the outer colonies have little to fight back with.
It's unlikely they would have been permitted large spacecraft and of course no overt weapons. They would have to fight dreadnoughts with laser and nukes using rail launchers and perhaps bioweapons.
There only real advantage would be that the earth powers would want to destroy the facilities and kill the workers unless they had to. They just want to regain control, especially of the technology. So, they'd only use the hammers when they had to. Otherwise they would just occupy. This would expose the to infiltration, bioweapons and computer hacking.
A lot of their attacks will resemble terrorism (but won't be if targeted at specific military targets or specific individuals carrying out operations.) But most readers won't understand that so you can add some moral ambiguity on the part of the colonist.
Politically, chaos merely means freedom. Freedom means that individuals can make decisions that others would not make. When there is no freedom, everyone has to make the same choice.
The problem is today that for people on the left, political freedom boils down only to matters of sex. You don’t' have freedom in jobs, business or any economics, housing, transportation, education, communications, reproduction no freedom. Used to leftist were big free speech advocate but no longer, so not even that. Just sex.
So, to make your colonials the good guys and the advocates of "freedom" just make their religion indifferent to or even actively promoting sexual promiscuity.
Meanwhile, ease in an awareness sexual restraint on the part of the earth government. Perhaps an attempt to control population. Maybe they give people drug to kill their sex drive so lose interest in loves and family, just have loose friends and devote themselves to work and the friends they make there. That's what a stereotypical fascist-corporation would do, right? Arrange for the perfect workers.
As long as the colonials have sexual freedom, they will be seen as the good guys even if they drop asteroids over half the earth. As long as their religion doesn't interfere with their sexual freedom or impose other restrictions on individuals it will be seen as a "good" religion.
People might at first see the earth government as the good guys, protecting the environment and regulating the corporations but once its revealed they don't allow sexual freedom, bang, instant bad guys.
Remember, making your story "understandable" means appealing to their existing prejudices and using common tropes.
I think your doing fairly well, The religious good guys is daring but just make it a self-esteem religion with no strictures and judgements and it'll be "understandable."