Fascinating, if sometimes uncomfortable, discussion. I have used Lovecraft in class, namely “The Shadow Over Innsmouth,” specifically because of how it deals with issues of race and class. Indirectly, often, but very much woven through the narrative. And really, in that story, the real horror Lovecraft intends for you is not the fish people, or the Deep Ones, but the fact that the narrator, who you think is a regular white dude like yourself (assuming at the time Lovecraft would be writing for white males mostly), turns out to be a fish dude himself! Horrors of miscegenation! One in the woodpile! Etc.
For me Lovecraftian fiction is at its heart about what folks upthread called cosmic terror, the sense of the futility of humanity in the face of the immensity of the universe, the total irrelevance of all human creations, religions, and beliefs, and the inevitability of our enslavement or destruction by vast forces that are all but incomprehensible to us. All the tentacles, bug-eyes, blobs, or whatevers are incidental to this psychological trauma. That makes the genre pretty much eternal.
As to the question of artist and their art, I am always conflicted. I’m Jewish but listen, occasionally, to Wagner, who I see as a brilliant composer as well as a wretched human being. I won’t listen to Ted Nugent any more because his current political activities annoy me (but he’s still alive, so there is a difference I think). Generally, as a historian, I try to view things with an eye towards context. I’ll read the Declaration of Independence, even agree with a lot of it, although I hear tell old Tom J. was a slaveholder. Every case is sort of different. Lovecraft is of an era, even if he’s a very extreme example of it in many ways, which doesn’t excuse him personally. His work exists, for me, as something both connected to him and separate from him. I would never use his work in class (or, I guess, in a game) without dealing with the context and unpacking a lot of the subtexts, though one would do that differently in different media of course.
There’s a ton of Lovecraftian fiction being written today by people of all races and gender identities (check out Caitlin Kiernan’s Black Helicopters, for instance, for an example), and I’m pretty sure these folks are damn well aware of Lovecraft’s racism and classism. In fact, they turn that on itself in their construction of horror within the Lovecraftian paradigm, often in very imaginative ways.