Nenhuma relação entre Cthulhu e Hastur foi mencionada em nenhuma das histórias originais de Lovecraft (acho que Lovecraft apenas mencionou uma vez Hastur em uma lista de nomes de entidades poderosas em The Whisperer in Darkness, veja a citação here ), essa rivalidade foi criada por August Derleth em suas próprias histórias de "Cthulhu Mythos" escritas após a morte de Lovecraft. Esta entrada em um wiki do Mythos diz:
Although Cthulhu is the best known figure in the pantheon, his alliance with the other mythos creatures in Derleth's stories is an uneasy one at best. At least one other Great Old One rivals his power and appears to be his personal enemy. That being is Hastur, Lord of the Interstellar Spaces, who currently resides in the Hyades. Although Derleth did not create Hastur, he did introduce him into the mythos as Cthulhu's half-brother and worst enemy. Various stories feature Hastur's cult assisting those trying to prevent Cthulhu from awakening. Other stories simply mention the rivalry between the two. In Derleth's "The Return of Hastur", first published in March 1939, the two gods even meet face-to-face, albeit briefly. This must be taken with a grain of salt, however, since many authors of Mythos fiction rarely dwell on this assumed rivalry, if they acknowledge it at all. It should also be noted that Hastur's domain is limited to a region far beyond Earth (Carcosa) and rarely impinges on Cthulhu's territory on Earth.
Eu diria que, se qualquer incidente claro desencadear a rivalidade nas histórias de Derleth, isso seria mencionado no wiki. Talvez seja apenas rivalidade entre irmãos?