Not necessarily so at all. As Lovecraft made abundantly clear in his voluminous correspondence, the major theme in his later writings was that of "cosmic outsideness", the existence of extraterrestrial, extradimensional, mostly baleful forces that are only temporarily held outside of the haven of our world and that these forces are continuously trying to break through, to man's ultimate detriment. Occasionally they suceed on a small scale, one day they will succeed totally. ("After summer comes winter, after winter, summer. Where man rules now, they will rule later.")
The partial embodiment of the break-through on the part of "aliens", the dark forces, is to be found mirrored in the "dark peoples" who were immigrating or might immigrate to America, as Lovecraft's descriptions of the revelers in tales such as "The Call of Cthulhu" make plain. When compared to his statements in correspondence on the decay and decline represented for him by the influx of "non-Aryans" into the old homesteads of the "native" WASP stock of New England, and even New York---(re)read "The Horror at Red Hook"---his stories about invaders---aliens---human or sub-/nonhuman, make perfect sense and are of a piece with his world view.
If you read some of Robert E. Howard's fantastic fiction you find the same---or, rather, a worse---kind of glib talk about "Aryans" and racial superiority. That's part of the point of these stories.
This was not so uncommon in the "Western" world of the time. The pre-WW II Western world saw the pinnacle of scientific racism, and it wasn't until the failed German model was revealed in all its loathsome glory that such thinking, such investigation, became unfashionable.
I have read and enjoyed both and I can say that the two are definitely akin. The theme of damnation runs through both authors' short story fiction. (Since going novelist, Barker's picked up on the theme of redemption, a natural thing for someone who's aging and wants to avoid the former.)
As you might imagine, where HPL only suggests horrors, Barker spells them in graphic detail. Sex with demons/aliens? "The Call of Cthulhu" and like Lovecraft tales suggest it by referring to "obscene rites" and the like. Or, it is verified by the presence of "hybrid" characters like Wilbur Whately (and his hideous sibling) of "The Dunwich Horror". In Barker you may expect somewhere along the line the phenomenon to be depicted, which is what you get in "Rawhead Rex".
If you want to see Barker's most Lovecraftian tale, a story that, except for its explicitness, could well have been written by Lovecraft himself, with its reference to a desert city of the damned, read or reread Barker's "In the Flesh" after you've read some Lovecraft. The parallels there are striking and undeniable, in my opinion.
Not hard. In the collection of short stories called . . . [drum roll] . . . In the Flesh (Pocket Books, 1986; I'm sure it's been re-issued since).
Mr. Barker also has a horror novel, which I bought finally about a year ago, but---surprise!---have yet to read, entitled The Damnation Game, which, according to Barker's Website, will be translated for the big screen. His other long stuff is either fantasy---with gore probably, I haven't read any of it---or deeply autobiographical, as I understand. Not horror.
HPL borrowed and incorporated some of the Chambers backstory into his "Cthulhu cycle". HPL's "Hastur the Unspeakable" made his (its?) first appearance, I believe, in Chambers's story, "An Inhabitant of Carcosa". ("Have you seen the Yellow Sign?")
I don't know whether "inspired" is the correct word here. HPL certainly borrowed from Chambers, Lord Dunsany (for his fantasy tales), and others, which he freely admits in his voluminous correspordence.
HPL's "Hastur the Unspeakable" made his (its?) first appearance, I believe, in Chambers's story, "An Inhabitant of Carcosa".
The first mention of Hastur as an entity was in Ambrose Bierce's "Haita the Shepherd". Bierce's "An Inhabitant of Carcosa" introduced Carcosa as a city and Hali as a prohpet. Chambers' "The Repairer of Reputations" and "The Yellow Sign" used Hastur as a city, Hali as a lake, and introduced the King in Yellow and the Yellow Sign.
Lovecraft's use of Hastur was quite fleeting. As you say, he was very fond of borrowing from others and liked to drop in names of places and entities for atmosphere. There are a couple of mentions in "Whisperer in Darkness", one in which he places Hastur directly between a list of various beings and a list of various cities and places. I think Lovecraft's influence here was from Chambers and that Hastur in Lovecraft was meant to be the city. Lovecraft makes a few other mentions of the King in Yellow and the Pallid Mask in various places, but the well-known Hastur the Unspeakable, half brother to Great Cthulhu, and sometime helper of humanity, was an invention of Derleth.
I'm not a fan of Derleth.