Here's my opinion on the whole supernatural interpretation of TD:
First postulate - TD takes place in the (a?) chamberian/lovecraftian universe. Second postulate - Rust has some form of ESP or psychic sensitivity.
The cultists were attempting to break out of "the flat circle". They were aware of the fact that they were trapped in this existence and wished to ascend from it. The child sacrifice and torture was how they were attempting to open the gateway out of our plane.
Reggie Ledoux: "I know what happens next... he literally does, because it's happened before ...You're in Carcosa now, with me...he sees Rust in Carcosa during episode 8, notice Errol says the same thing while Rust is chasing him... He Errol sees you. You'll do this again. Time is a flat circle.
Ledoux wasn't just spouting gibberish. He had achieved some measure of success with escaping the "flat circle" of his existence. Although he and Rust were never at Carcosa together from our temporal reference, from his fourth dimensional perspective time is flat and they are indeed there simultaneously
Errol: "My ascension removes me from the disc in the loop. I'm near final stage, some mornings I can see the infernal plane".
Errol is also having success in breaching our plane. He seeks to be removed from his infinitely repeating existence (the disc in the loop).
When asked where Bill Childress is, Errol's,umm...girlfriend?...responds: “All around us, before we were born and after you die". In other words, you guessed it, time is a flat circle. He existed before us and will exist again after we're gone, when the disc comes back to that particular part of the loop.
When Rust and Marty pull up at the Childress residence, Rust can sense that "this is the place". His ESP is perceiving something (the souls of all the dead there?). This feeling is conveyed to the audience via a series of strange haunting sounds. That wasn't just a creepy soundtrack, it was the disturbing psyhcosphere of the area put into auditory form so that we could hear what rust was feeling.
When he finally makes his way to the inner chamber of Carcosa, he is able to perceive the breach created by the cultists. The giant swirling vortex is not a hallucination. It is a gateway to another plane beyond our existence and the genesis of the swirl symbol used by the cultists. They could see it too, or at least one of them had seen it.
Errol Tuttle says 'my family's been here a long time'. Given that Carcosa appears to be a pre-civil war French era fort, possibly a pirate garrison at one time, in a Bayou/ Littoral zone we can assume the early vestiges of what became the cult are as old as the coast's European settlement. Originally, I think the inhabitants of the fortress were pirates from whom some of the cult members trace their ancestry who were around since the early 1700s. These pirates have been there a long time, since at least the mid 1700s French colonial period. The French era rule would also explain the Cajun Mardi Gras motifs we glimpsed in the video. Moreover, like in the Pitcairn Islands, longstanding cults of child sex abuse are a thing that isolated pirates and their ancestors do. Perhaps, over the course of the 1800s and as a result of interaction with West African slaves and Spanish influences, Voudon and Santaria entered an ingrained culture of pedophilia which also merged with Mardi Gras and Acadian/ Cajun Catholic pageantry. As this family/ cult/ set of families, possibly including creole and black branches, evolved its culture of pedophilia, some distinct elements of West African sun worship, and the sacrifices therein, began to occur. Hence why the sacrifices follow solstices and harvest festivals.
I'm really glad they didn't reveal anything like the cult's history as it makes it a truly Lovecraftian and unseen horror (and allows us on the internet to speculate indefinitely). But I think that when Cohle says he sees, 'sprawl' what he's looking into is an abyss, an ingrained evil that's older than the very State of Louisiana which he once served. The cult, is as mysterious as the Bayous, the coast, and Southern Louisiana's/ Acadiana's early history. It's a sinister centuries old throwback that was engulfed by swampy overgrowth and stayed hidden there becoming an unseen part of the coast's culture and way of life. Very much an homage to Ambrose Bierce's Carcosa, it no longer exists, but there are still people from there. It's a wretched place, and its tentacles and legacy persist to pollute our world.
TLDNR; The cult probably have their origins in piracy and are a part of the Louisiana Coast's storied history of cultural cosmopolitanism. It's cool that the creators never explained any of the 'Sprawl' because it fits with the writing and inspirations for the series.