Cosmic horror is a genre. The dead man known as Lovecraft has no hold over it unless you choose to give him that power.
He doesn't even have any power over his own work (aside from the whole 'being dead' thing) due to it being public domain, that's why so many artists, writers, directors and game designers use his monsters and uncaring universe while ditching his vile social views.
This also allows for subversion- Winter Tide by Ruthanna Emrys reimagines Shadow over Innsmouth as a short prequel, with the narrator described as a racist bigot, and that tale's ending leading to Deep Ones and Innsmouth residents in Internment camps alongside the Japanese in WWII. This leads to, in modern times, a descendant of the Innsmouth prisoners living with a Japanese family in the US. It takes an alternate cosmic viewpoint from the perspective of an immortal species, that makes petty human bigotry seem pointless- ultimately both Deep Ones and humanity are equally doomed on a galactic timescale, our underwater cousins just have gods that answer their prayers and seem terrifyIng to those of us that stumble across them. To the viewpoint of the more-alien Yith, both groups are more similar than dissimilar, with humanity obsessed with minor differences while they enigmatically try to preserve knowledge from foes across the entirety of time and space. Cultists are still the bad guys, but with humans torturing Deep Ones by denying them water, desperate for info on what else is out there that they just don't have, and the scared authorities desperate for control taking risks with things they don't understand, it's quite a refreshing take on the subject matter that condemns HPL's bigotry while taking some of his best-known creations for a spin.
Same goes for Charles Stross, whose 'The Laundry' series of spy fiction crossed with the Mythos is rapidly reaching its endgame. Awesome tales that re-examine a lot of themes, and again ditch the xenophobia due to the fact we can communicate with the earthbound factions making for some shakey alliances against greater threats.
Disallowing the Cthulhu Mythos because HPL was a racist would mean no such analysis, subversion and challenging of his views. Same goes for other authors- most recently Revival by Stephen King was clearly influenced by HPL's work, and Darkest Dungeon's 'rummaging around beneath the crumbling family manor, obsessed with legacy' is absolutely Lovecraft too. I struggled to see any influence of Lovecraft's racism in the final products, just influence from story themes that have been far removed from it by creatives that loved the latter and left the former to rot.
