Now all my tales are based on the fundamental premise that common human laws and interests and emotions have no validity or significance in the vast cosmos-at-large. To me there is nothing but puerility in a tale in which the human form—and the local human passions and conditions and standards—are depicted as native to other worlds or other universes. To achieve the essence of real externality, whether of time or space or dimension, one must forget that such things as organic life, good and evil, love and hate, and all such local attributes of a negligible and temporary race called mankind, have any existence at all. Only the human scenes and characters must have human qualities. These must be handled with unsparing realism, (not catch-penny romanticism) but when we cross the line to the boundless and hideous unknown—the shadow-haunted Outside—we must remember to leave our humanity and terrestrialism at the threshold.
— H. P. Lovecraft, in note to the editor of Weird Tales, on resubmission of "The Call of Cthulhu"
The conflict in Lovecraft is between the stated aim of an externalised perspective on human affairs ('one must forget that such things as... good and evil, love and hate... have any existence at all") vs. his personal horror at such a state of affairs ("the boundless and hideous unknown").
What's most important in his stories isn't the (supposed) indifference of the universe so much as our (supposed) horror in the face of it.