I am very interested to hear what our more religious members have to say about the concept of the stack [serious]

I honestly don't think religious people watch shows like this or contemplate questions like you're asking. It's too challenging to their worldview.

Basically, what the show tells us that humans discovered a way to clone not only bodies but also the souls, which impossible in most major religions. Only God has that power. The soul does die with the 1st iteration and what you're left with is a copy of you but not really you, because the soul doesn't transfer thru stacks. You can't digitize, capture and download it. Also, it doesn't need a body to exist but it needs a body to be in the world of the living. There are different worlds you see, the world of souls before birth, the world of the living and the Afterlife.

Stack, changing sleeves etc. is not technically possible at the moment. So... evaluating all this from a religious point of view would be some sort of a speculation and science fiction of its own. However, as to the very concept of the stack - it could be analyzed from a modern social, psychological etc. perspective.

What is changing sleeves? Nothing more than a desire to remain physically immortal and a fear of physical death tunnelled into a SF concept. Most religions consider physical bodies to be but a small part of human experience and thus criticize clinging to pure physical existence labelling such desire as 'satanic'. Also, every founder of the three 'universal religions' had to embrace death at a certain point in his life thus becoming an example for the followers.

Somehow maintaining your physical body through the ages is just a remix on a medieval legend of 'wandering Jew' (which in turn was a form of critique of the physical immortality).

We got into debates about this years ago with Star Trek. The transporter essentially murders you every time you step into it, and reproduces you far, far away. Everytime you transport, you're becoming a copy of yourself. How does one's soul know how to stay attached or follow you? Does a severed soul recognize you, even far away and just sling back into you like a bungee cord? Or do you lose your soul the first time you transport and now you're just a flesh robot rambling through the cosmos? The question becomes even deeper with Altered Carbon and entirely different bodies introduced. IMO, that soul has left the building, only the memories remain, but that doesn't mean another soul isn't merged with the body. Assuming souls are required for life.

I think people lose their souls all the time. I think they're interchangeable. I also believe in the OverSoul and a whole ton of crazy other crap. I think souls are made of basically The Force, the glue of universe, dark matter maybe, and like ectomplasmic ghosts it manifests and possess and sparks life every time anything lives anywhere. If the memories are strong enough, this impression, this rogue soul remains instead of returning to the "soup", and you get people who wake up one day with different personalities. Or the notion of reincarnation, if you will, in a fresh birth.

A person who believed in a soul would likely believe this technology would never be possible.

This all comes down to the question of soul. Religious people might believe this technology would never even work because the soul wouldn't transfer. Others might believe the consciousness IS the soul. I think an interesting extension of this question is as it relates to ai becoming aware, when they start to "feel," and care and love. Some people would believe that couldn't happen . . . but what if it did? That would have to change our whole understanding of soul and humanity. DesCartes said "I think, therefore I am," but we have computers now that for all intents and purposes do think. Amazon's Alexa can hold a more intelligent conversation than some people I know. A more appropriate phrase should be "I feel, therefore I am." When ai, or clones, or replicants, or androids, or whatever can love us back, will they have a soul?

I don't think our more religious members would care to respond. If you allows, I would like to give a try. My opinion is a stack stores the digital copy of one's soul. From a religious point of view, blowing the soul (breath of life) into the body is considered as one becoming alive; And when the soul leave the body, it is considered as one's death. To those future human replicant, putting one's stack into a sleeve is considered his/her resurrection, in other words, becoming "alive". And when the replicant die, they take out the stack and then put into a new sleeve if he/she can afford that or deserve that.
Obviously, the digital copy of a soul is not a real soul, just like a human replicant is not a real human. Those being in the altered carbon world might need an altered religion to deal with that.

The stacks and sleeves issue is disturbing. The show goes to point out that having "two versions of the same stack around at the same time is punishable by perma-death". The russian guy made a copy of himself and called eachother brothers, but it was the same memories and same person but two of them same time alive. This was important to show, because it establishes that in actuality those stacks make copies of your memories like a data storage. So its not really YOU, its just a data copy of your memories. Which is why the russian could have two versions of himself. So all those stacks and sleeves are copies of copies. The real person died a long time ago.

I wouldnt want a copy of myself walking around after I die. It wouldnt be the real me. Even if it had my memories.

So I was repulsed by the idea and premise. Its a cold evil world, where the sociopathic elite rule forever with stacks of wealth. Copies of people walking around that arent the real people. Its an affront to the natural order and mars the beauty of our existence. We arent meant to live here forever and we are meant to die. We die so others may get the chance to live.