This has come up before in another thread (link), but the way I think of CoC cultists has evolved since then. Now, I would say that the word "cultist" in Call of Cthulhu is mostly a red herring, a distraction, disinformation spread by unreliable narrators.
What we're referring to as "cultists" are not, in the traditional sense, actually cultists.
These are instead probably ordinary people who have suddenly discovered some monstrous intrusion into their lives, and are dealing with it as best as they can.
As a result, "ranting like a cultist", I believe, would sound a lot like the sort of thing that any ordinary people do when trying to deal the best they can with situations that are impossible to deal with head-on.... expect a lot of excuse-making, self-justification, apparently sincere claims that the "Mythos" isn't that bad and the "cult" can stop doing bad things any time it wants, that it's "only" one sacrifice every full moon, that the problems are blown out of proportion by "haters" or whatever, that the Deep Ones are usually easier to get along with than humans are and the "cultists" and their victims are responsible for all the horrors and abuses and indignities the Deep Ones heap upon them, that the "progress" and "benefits" being made by the discovery/scheme/monster/whatever far outweighs the risks and costs, that Cthulhu is Hope, that freedom from the Mi-Go is slavery, that normal governments and mild Earth religions are far worse than anything the Cult of Nyarlathotep has ever done, that it's the investigators' fault that the "cultists" have to resort to violence because the investigators were nosy/mind their own business/courageous/cowardly/violent/peaceful/whatever, that it's not the "cultist's" decision to do whatever awfulness the cultist is doing but instead the cultist has no choice, that the cultist is just following orders, if the cultist doesn't do the awful things then the "Mythos" will find someone even worse to work with, that the cultist is doing the investigators and the world a favor by doing awful things, that there's worse things the "cult" might be doing, that some sort of end (maybe not even one offered by "the Mythos") justifies the "cult's" means and the cult's awfulness will make everything better in the long run if just a few "small" sacrifices are made, that if nobody upsets the "Mythos" and does what it says then the "Mythos" will (mostly) leave everyone alone, that the "cultists" deserve the "privilege" of doing something a little awful every now and then, that the "cultists" bear an uncommon and lonely "responsibility" to do awful things for everyone else's own good, etc.
Consider your typical investigators with a few scenarios behind them: they've probably left a trail of bodies behind, have probably gotten a few "close friends" and "long lost relatives" killed in one way or another, have probably burned down a few buildings, have perhaps made a questionable alliance or bargain or two, have read a couple foul and sanity-blasting books of forbidden lore, have perhaps cast one or two horrible spells, have committed a number of home invasions and illegal searches-and-seizures, have broken numerous gun laws, have lied to authorities, have concealed evidence and threatened witnesses, etc.
If you were to ask them whether they are heroes or villains, those investigators would probably insist they are heroes - and, if you were to ask them to describe the "heroic" things they've done, or to explain the trail of death and destruction they've left behind them, think about what the investigators might say. Chances are good that those same sorts of things would probably be the sorts of things that Call of Cthulhu "cultists" might "rave" about.
If you think of each cultist as the hero of his/her own Call of Cthulhu horror story, trying to do the best he/she can do, or perhaps trying not to "rock the boat", or at least trying not to make things worse, then I suspect their rants will start to write themselves.
"We didn't have a choice: we had to sacrifice a few children to Shub-Niggurath. We'd had one bad harvest too many, and we were about to starve - it was either make a few sacrifices here and there, or see EVERYONE starve! It wasn't easy making the choices we had to make, but after the first child was... was 'blessed' by the Goat, and the harvest came in stronger than ever, we knew we'd made the right decision. It's easy for YOU to say we did the wrong thing, but you didn't have to see starving children - a deal with Shub-Niggurath is a small price to pay, and we'd all pay it again. Or, most of us would - not everyone agreed, some wanted to go to the state authorities, but we couldn't let that happen; we didn't want to kill anyone, nobody wanted to do that, but the whistle-blowers forced us to silence them - if only they'd kept the oath! We tried to make it quick and painless, but it wasn't our choice, what the Dark Young did to them... and what we did, we did for the children! If we'd gotten raided and arrested or killed, what would have happened to the children we'd saved from starvation? Do you know what they do to children in your city orphanages? Better to lose a couple whistle-blowers, than to abandon our kids to a fate worse than death... and better to live with a little blood on our hands than to lose the whole town. But then you city people had to go and poke your nose where it didn't belong! We had things under control here, we'd come to an arrangement, and Shub-Niggurath wasn't that hard to deal with, until you showed up... it could have been a better world, all we needed was another harvest or two to get back on our feet, we could have sealed the bargain and closed the portal forever, but then you showed up, and we had to set the Dark Young loose to stop you, and now She is on her guard, now we owe Her even more, and the Black Goat changed her bargain, and now thanks to you the High Priest is dead and nobody can close the portal without making a new bargain, with a new priest! At least the last priest was mostly human - we're not quite sure what the new high priest is! You're lucky we're killing you, and not the new High Priest... Ia! Shub-Niggurath! You think the Dark Young are bad? Pray that you never have to hear that priest's voice, or see the shadows it casts upon the veil it hides behind!"