Virtually all modern stories set in the Cthulhu Mythos assume the protagonists of Lovecraft's original stories were Unreliable Narrators due to their racist views. Another interpretation that's been used in stories like The Ballad of Black Tom and Lovecraft Country is that racial minorities are more willing to deal with the Eldritch Abomination not because they are "primitive," but because they are desperate.
Lovecraft was rather vague about Azathoth in his writings, with much information about him coming from later writers for the Mythos. Perhaps he lost his sanity in an untold cosmic war, perhaps he's subordinate to an even more powerful god we can't begin to imagine. One interpretation is that, seeing how the whole Mythos exist within Azathoth's dreams, perhaps Azathoth is the reader themselves with the Mythos existing in our imagination?
August Derleth's contributions to the Mythos are probably the most divisive. On the one hand, there are numerous fans who will never forgive Derleth for ditching Lovecraft's Blue-and-Orange Morality in favor of Black-and-White Morality. On the other hand, there are still many who find his stories enjoyable, and some of his creations (e.g. Ithaqua) and ideas (e.g. Hastur being one of the Great Old Ones) remain popular. The fact that Derleth's work was hugely influential to a whole generation of Mythos writers only adds fuel to the debate.
In general, how valid in the Cthulhu Mythos that weren't originally written by H. P. Lovecraft, then and now? Derleth is only the tip of the iceberg — some will allow anyone but Derleth's stories, despite Derleth being a contemporary of Lovecraft with an established rapport, while others will only include Lovecraft's initial circle, and yet others will only accept Lovecraft's own stories. Reasons range from Only the Creator Does It Right for Lovecraft-only readers, a preference for works made with Lovecraft's input, to Derleth injecting mere morality into a universe that repeatedly revolves around the idea that These Are Things Man Was Not Meant to Know and is inherently hostile to human life a bad attempt at making it Lighter and Softer.
Common Knowledge: There are many misconceptions about the Cthulhu Mythos, usually perpetuated by later writers such as Derleth.
First among them is probably the prominence of Cthulhu himself. He makes a good mascot, but in the context of the original stories he was never a particularly important or powerful character. He was simply a priest of the Great Old Ones who got knocked out by a steamboat. Derivative works portraying him as a kind of solo god or even a beast also forget that At The Mountains of Madness established that he spawned (and presumably led) an entire race of space-faring conquerors, meaning he's very much a sapient Sufficiently Advanced Alien.
The second biggest is the idea that Lovecraftian abominations could all drive people crazy as a result of some kind of power, as if they could drain a video game Sanity Meter. There is very little evidence for this in the text itself. It is true that losing one's sanity is a common enough occurrence in Lovecraft's works, but it doesn't always happen to characters who saw an Eldritch Abomination. Some simply can't handle the existence of comparatively mundane fish-men, ape-like creatures or cannibal cults either (as in The Shadow over Innsmouth, "Arthur Jermyn", and "The Rats in the Walls", respectively), and it helps that many Lovecraft characters are mentally weak to begin with. As for the eldritch beings, some of them, like Cthulhu, are known to mess up with people's dreams, but the notion that the mere sight of them would break anyone's mind is, at best, an exaggerationnote of the two sailors who survive the encounter in "The Call of Cthulhu", one does go mad and dies from something that might be an aneurysm or stroke, but the other recovers quickly and escapes. Besides that, many of Lovecraft's protagonists simply never went insane at all, even after encountering or punching out cosmic monstrosities, like in "The Dunwich Horror". Whenever a protagonist genuinely did Go Mad from the Revelation, it was usually after a prolonged period of physical and mental duress, of which the sight of the horror is simply the final straw, as in At the Mountains of Madness and "Dagon". Even then, of the two characters from At the Mountains of Madness who actually saw the shoggothnote on top of trekking for ages in the harsh Antarctic mountains, losing members of their party, being deprived of sleep, water, and food, and learning that mankind was created by aliens, only one of them went mad from the experience, and wound up mostly being successfully treated for it. And that was only after seeing something else that he won't tell anyone about. Simply learning about the Great Old Ones, or seeing them without any context, does nothing to one's sanity whatsoever. One character carefully pored through the Necronomicon several times and kept his sanity intact, as he viewed it no different from any mythological text which describes things that do not really exist. Heck, one Great Old One (Rhan-Tegoth) was able to be stuck in a wax museum disguised as a statue, and no one even caught on to the fact that he wasn't wax, much less went insane just from looking at him.
The idea that humanity was totally insignificant before various alien horrors. While it was key to Lovecraft's works that we were insignificant, what seems to be missed in the pop version is that so were the alien horrors. Not all of them were Azathoth or Yog-Sothoth. More often than not, the protagonists would stop or at least survive whatever the alien threat was. Even Nyarlathotep wasn't immune to getting tricked by a human, to the point that The Dream-Quest of Unknown Kadath ends with the Crawling Chaos brooding over his defeat. Call of Cthulhu has a cultist remarking that, while the rise of the Old Ones can't be stopped, by the time they come back we'll have learned so much and would have become so powerful that "mankind would have become as the Great Old Ones", albeit with the implication that the cultists believe humanity would need to be as amoral as how they perceive the Great Old Ones to attain power.
Creepy Awesome: Any and all of the gods. Even Nodens, who has been known to protect humans occasionally, still has the sinister title of Lord of the Great Abyss.
Cthulhu has so little role in Lovecraft's work, yet is the most famous now. The fact that he lent his name to the franchise should be evidence enough. It helps that Lovecraft himself seems to have been fond of him, as he often name-dropped Cthulhu in his writings (including his own stories, his revisions, and letters to his friends).
Despite showing up in about two Mythos stories, Cthylla is pretty well known.
In more recent years, Y'golonac has been gaining some popularity, though he's only appeared in one "official" Mythos story so far.
Evil Is Cool: Nyarlathotep. Even in the original stories, in which most of the gods are more accurately described as indifferent to mankind than outright evil, he was presented as a manipulative Faux Affably Evil figure, which makes him stand out from the crowd and contributes to his popularity.
Nyarlathotep's often called "Nyarly" or "Gnarly" by his fans.
"Big C" for Cthulhu.
"Shubby" for Shub-Niggurath.
Fanon: A lot of the "mythos" could be considered this, since so much was built up by later authors, rather than Lovecraft and his contemporaries. Of particular note is the belief that "Dagon" is a Lovecraftian God and a servant of Cthulhu. Pretty much any reference Lovecraft makes to "Dagon" in his own stories could be read as in-universe mythological allusions, out-of-universe mythological allusions (both of which presumably to the Canaanite deity named Dagon who is mentioned once in the Bible), or a code name used by Cthulhu worshippers to avoid attracting attention.
Fanon Discontinuity: While there are plenty of canon disputes within the fandom, Bloch's "Shadow From the Steeple" is commonly held in low regard.
Fanwork-Only Fans: Many people are fans of the Cthulhu Mythos and its many related works while avoiding the original stories of H. P. Lovecraft that inspired it, rejecting the works for the author's racism and xenophobia. Indeed, some popular works such as Lovecraft Country and The Ballad of Black Tom can easily be described as Deconstruction Fic for Lovecraft's white supremacist perspective.
Friendly Fandoms: The franchise is popular with Heavy Metal fans and artists and said genre has been one of the most prolific mediums when it comes to representing Cthulhu and its mythos to the fandom's appreciation, thanks to songs like The Thing That Should Not Be by Metallica, Behind the Wall of Sleep by Black Sabbath, Horror of Yig by GWAR, Thy Horror Classic by The Black Dahlia Murder, and Beneath Oceans of Eternal Sand by Nile.
Lovecraft described Azathoth as a monstrous indescribable thing which resides in the center of the universe, often described as "gnawing" and "chaotic". Scientists now believe that the center of our galaxy (and, by extension, other galaxies), is a supermassive black hole. Perhaps Lovecraft was on to something...
In the 1931 short story The Lair of the Star Spawn by August Derleth and Mark Schorer, the characters manage to stop the Great Old Ones Lloigor and Zhar with the aid of the Star Warriors from Orion, described as monstrous-size glowing beings that "shot great beams of annihilation and death". In 1966, Tsuburaya Productions created the Ultra Series, a toku series about heroic aliens, also known as giants of light, with many abilities, including shooting powerful beams from their arms. And by sheer coincidence, their homeworld is located in Nebula M78 in the Orion Constellation. Doubly hilarious after their 1996 entry Ultraman Tiga, which featured Ghatanothoa as the Big Bad, complete with Lloigor (or Zoiger in this case) servants and an appearance from R'lyeh.
Inferred Holocaust: The bodies most commonly associated with the Yithians? Those belonged to beings native to Earth before the Yithians used their mind-swapping powers to leave their own dying world for ours...
It's Popular, Now It Sucks! : Some consider the character of Cthulhu to be so overused and well-known that he's become a cliché of the Cosmic Horror Story genre. Fortunately, there's plenty of other monsters and villains in the Mythos for writers to use to avert this.
Mainstream Obscurity: Plenty of people probably have heard of Cthulhu, but have not read Lovecraft.
Memetic Badass: An interesting version of this with Azathoth. He is already a “badass” in the mythos (Being the one who dreamt into reality absolutely everything in existence), but when it comes to online discussions regarding character power levels Azathoth will always be used as a prime example of a (practically) omnipotent character, requiring other candidates for the title of “strongest character ever” (Like The One Above All and Kami Tenchi) to beat him.
Lovecraft's Cat's NameExplanation His cat was called, well, read it for yourself. Because of how horribly racist it is, it's common for people to dance around the issue of the cat's name and treat it as eldritch knowledge that can drive a man mad.
Mysterious colors unlike anything seen on Earth Explanation A phrase often repeated in some of Lovecraft's works, particularly The Colour Out of Space. Often mocked for being a ridiculous concept, since a color unlike anything we've seen on Earth would probably not be visible to human eyes.
Non-Euclidian Geometry Explanation Used by Lovecraft and others, like Frank Belknap Long, to describe supposedly impossible or strange angles.
Hastur originally came from Ambrose Bierce's Haita the Shepherd. Chambers used the name in The King in Yellow. In spite of Hastur's prominence in the works of later Mythos authors, H. P. Lovecraft only used it once as a casual name-drop in "The Whisperer in Darkness".
The term Fire Vampires were first used for Fthaggua's servitors. Later, Lin Carter used the term to describe Cthugha's Flame creatures, and it became the depiction that most associate with, popularized by Call of Cthulhu.
Praising Shows You Don't Watch: Receives a lot of praise from people who know little about it besides that it's where Cthulhu comes from.
One could consider the interbreeding between humans and the Deep Ones to be this since it's basically people having sex with giant fish.
Values Dissonance: There's no real beating around the bush; Lovecraft himself was an unabashedly racist man even by the standards of the era he was born into, and this, unfortunately, reflects a lot in his writing. 'Savages' is one of the nicer words he uses to refer to non-white people, and racial slurs being thrown around by his protagonists are unfortunately really common, as is (almost) every non-white character in his stories either being a villain, or part of a cult for one of the elder gods. Even the rare sympathetic portrayals, such as Chief Grey Eagle, still have racist tropes attached to them (in his case Magical Native American and Tonto Talk). Needless to say, this can make getting into the mythos by reading his original writing incredibly uncomfortable.
in Japan to the point that it had a huge influence on many Japanese works.