I see this said all the time and I think it's almost entirely wrong.
(Short version: those parallels aren't terribly close and one can find plenty similar parallels in things that no one thinks are religion-like. Long version: read on.)
"Roko's Basilisk is just rewarmed Pascal's Wager". I don't think it really is, but in any case it's something that so far as I can make out rationalists generally don't agree with and don't give any thought to except when it gets trotted out yet again as an illustration of how crazy rationalists are.
"The singularity is just the apocalypse / rapture". Both are hypothetical future events that would change the world a lot. Beyond that the match doesn't seem very close. The Christian apocalypse narrative is, above all else, about Good Versus Evil. A battle between God and his enemies! A grand judgement in which the living and the dead are all consigned to eternal bliss or eternal destruction! Us against Them! And there's none of that in what people say about technological singularities. (Well, except for Roko's basilisk, I guess. But, again, that isn't actually a thing anyone believes in or gives any thought to.)
"High priests (tech CEOs)". I don't think I've ever seen anything written by rationalists that treats tech CEOs as high priests. Here are a few quotations from recent highly-upvoted Less Wrong comments from high-karma LW users; each was the first thing I found in a search that seemed like it was expressing any sort of opinion on the CEO in question: "Sam Altman has systematically dismantled all of OpenAI's oversight, and betrayed the promises OpenAI made to humanity." "I would add that Elon Musk is not trustworthy and has been strongly suspected of manipulating the recommendation of X ..." "The best executives are very strong generalists, and the best managers are chosen to be strong performers in the task that they are managing other people to do. Elon is widely known to be a strong engineer, as well as a strong designer, and spends much of his time arguing details of that kind of work with his reports. Mark Zuckerberg is known to do similarly." First two are very strongly negative. Third is positive but a long way from setting either of the people involved up as high priests. I didn't find anything very specifically pro or con Satya Nadella, Sundar Pichai, or Jeff Bezos.
(A lot of internet-rationalists were pretty keen on Elon Musk back in the day, but so were a lot of other people. And there was an infamous post in which Yudkowsky wrote about how major-company CEOs and hedge fund managers and eminent professors seemed really impressive when he met them, which is cringey but not obviously wrong and in any case falls well short of calling anyone high priests -- and the comments below it are full of people saying things like "have you considered that maybe one way you get to be a CEO is by being good at looking impressive?".)
"theologians (Yud, SA)": if "theologian" just means "person who thinks about things and whose writings are respected" then, sure, Yudkowsky and Alexander are "theologians", but then literally every field will have its "theologians". Donald Knuth wrote some big books that everyone respects, and sometimes the word "bible" is attached to them! Clearly he's a theologian and computer science is just another religion! (Actually, Knuth is a theologian, a little bit; see https://archive.org/details/316bibletextsill0000knut.)
"sacred texts": see above.
"heresies (logical fallacies)": heresies are doctrines that arise within a particular religion and are officially rejected by it; to anyone outside the religion they're an irrelevance. Logical fallacies are definitely not that. If someone mixes up "A implies B" and "B implies A" or something, you don't need to be an internet-rationalist to think they're wrong or to criticize their argument.
You might be able to make an argument that Roko's basilisk is an example of a heresy within rationalism? But I don't think the existence of inside-baseball debates where some positions are officially deprecated is terribly specifically religious. The idea that goto statements are a great way of structuring a piece of computer software would be a heresy, for instance. Belief in "cold fusion" would be another. But computing and physics aren't religion-like in any useful sense on that account.
(Short version: those parallels aren't terribly close and one can find plenty similar parallels in things that no one thinks are religion-like. Long version: read on.)
"Roko's Basilisk is just rewarmed Pascal's Wager". I don't think it really is, but in any case it's something that so far as I can make out rationalists generally don't agree with and don't give any thought to except when it gets trotted out yet again as an illustration of how crazy rationalists are.
"The singularity is just the apocalypse / rapture". Both are hypothetical future events that would change the world a lot. Beyond that the match doesn't seem very close. The Christian apocalypse narrative is, above all else, about Good Versus Evil. A battle between God and his enemies! A grand judgement in which the living and the dead are all consigned to eternal bliss or eternal destruction! Us against Them! And there's none of that in what people say about technological singularities. (Well, except for Roko's basilisk, I guess. But, again, that isn't actually a thing anyone believes in or gives any thought to.)
"High priests (tech CEOs)". I don't think I've ever seen anything written by rationalists that treats tech CEOs as high priests. Here are a few quotations from recent highly-upvoted Less Wrong comments from high-karma LW users; each was the first thing I found in a search that seemed like it was expressing any sort of opinion on the CEO in question: "Sam Altman has systematically dismantled all of OpenAI's oversight, and betrayed the promises OpenAI made to humanity." "I would add that Elon Musk is not trustworthy and has been strongly suspected of manipulating the recommendation of X ..." "The best executives are very strong generalists, and the best managers are chosen to be strong performers in the task that they are managing other people to do. Elon is widely known to be a strong engineer, as well as a strong designer, and spends much of his time arguing details of that kind of work with his reports. Mark Zuckerberg is known to do similarly." First two are very strongly negative. Third is positive but a long way from setting either of the people involved up as high priests. I didn't find anything very specifically pro or con Satya Nadella, Sundar Pichai, or Jeff Bezos.
(A lot of internet-rationalists were pretty keen on Elon Musk back in the day, but so were a lot of other people. And there was an infamous post in which Yudkowsky wrote about how major-company CEOs and hedge fund managers and eminent professors seemed really impressive when he met them, which is cringey but not obviously wrong and in any case falls well short of calling anyone high priests -- and the comments below it are full of people saying things like "have you considered that maybe one way you get to be a CEO is by being good at looking impressive?".)
"theologians (Yud, SA)": if "theologian" just means "person who thinks about things and whose writings are respected" then, sure, Yudkowsky and Alexander are "theologians", but then literally every field will have its "theologians". Donald Knuth wrote some big books that everyone respects, and sometimes the word "bible" is attached to them! Clearly he's a theologian and computer science is just another religion! (Actually, Knuth is a theologian, a little bit; see https://archive.org/details/316bibletextsill0000knut.)
"sacred texts": see above.
"heresies (logical fallacies)": heresies are doctrines that arise within a particular religion and are officially rejected by it; to anyone outside the religion they're an irrelevance. Logical fallacies are definitely not that. If someone mixes up "A implies B" and "B implies A" or something, you don't need to be an internet-rationalist to think they're wrong or to criticize their argument.
You might be able to make an argument that Roko's basilisk is an example of a heresy within rationalism? But I don't think the existence of inside-baseball debates where some positions are officially deprecated is terribly specifically religious. The idea that goto statements are a great way of structuring a piece of computer software would be a heresy, for instance. Belief in "cold fusion" would be another. But computing and physics aren't religion-like in any useful sense on that account.