An upside down cross has always been the cross of st Peter, but when (or how) did it become a satanic symbol?
In the late medieval and early modern period "Satanism" was understood as involving a deliberate inversion or mockery of Christian rites, for example:
In a town which is better not to name, for the sake of charity and expediency, when a certain witch received the Body of Our Lord, she suddenly lowered her head, as is the detestable habit of women, placed her garment near her mouth, and taking the Body of the Lord out of her mouth, wrapped it in a handkerchief; and afterwards, at the suggestion of the devil, placed it in a pot in which there was a toad, and hit it in the ground near her house by the storehouse, together with several other things, by means of which she had to work her witchcraft.
They also performed a travesty of the Mass, celebrated by one clothed ina black cope with no cross woven upon it. At the time of the Holy Sacrifice and the Elevation of the Host, he lifted up a segment or round of turnip stained black, upon which they all with one voice cried out: "Master, help us!" The Chalice contained water instead of wine; and they made their Holy Water as follows:--The goat pissed into a hole dug in the ground, and with this undiluted water the celebrant sprinkled them all with a black aspergillum.
The latter of which is recognizable as a version of what became known as the "Black Mass" or "Satanic Mass." The Black Mass formed a key scene in an influential French novel of the 19th century: Là-bas (1884) by Joris-Karl Huysmans, who included among his Satanic imagery:
"But," said Durtal, "permit me to ask you several questions. Certain details interest me. What were the sacerdotal ornaments of Dr. Johannès?"
"His costume was a long robe of vermilion cashmere caught up at the waist by a red and white sash. Above this robe he had a white mantle of the same stuff, cut, over the chest, in the form of a cross upside down."
"Cross upside down?"
"Yes, this cross, reversed like the figure of the Hanged Man in the old-fashioned Tarot card deck, signifies that the priest Melchisedek must die in the Old Man—that is, man affected by original sin—and live again the Christ, to be powerful with the power of the Incarnate Word which died for us."
Some of these sources took their time to filter into English, but by the late 1920s and early 30s were fairly available to audiences in the United Kingdom and United States - and definitely entered the popular fiction of the time as it related to Satanic cults and witchcraft. You can see this in many pulp stories, such as this example:
"Mockery, Messer," said the mage softly. "the furs of panther, lynx, and cat are worn always in these rituals. And those candles, Highness," he went on, turning now to the Prince Borgia, "those candles are made from the fat of corpses. see too how they are made, each in the form of an inverted cross. Their bowls are skulls, and their fires are fed with cypress branches, and with the wood of gibbets. Soon they will consecrate a black host before that huge inverted cross they have stolen somewhere."
Derleth was, by-the-by, a good Catholic who later received the Apostolic Blessing of Pope John XXIII for his part in writing a series of religious books for children!
Anton LeVay, founder of the Church of Satan, made a point about the popular image of the Black Mass:
the popular concept of the black mass is thus: a defrocked priest stands before an altar consisting of a nude woman, her legs spread-eagled and vagina thrust open, each of her outstretched fists grasping a black candle made from the fat of unbaptized babies, and a chalice containing the urine of a prostitute (or blood) reposing on her belly. An inverted cross hangs above the altar, and triangular hosts of ergot-laden bread or black-stained turnip are methodically blessed as the priest dutifully slips them in and out of the altar-lady's labia. [...]
LeVay is clearly borrowing left and right from various sources to make as despicable image of the whole image as he can, then goes on to explain that this is all propaganda by the church--and in fact while LaVeyan Satanism does include a Satanic Mass, it is not in any way theistic and is considerably tamer (not to say more sanitary) than the above.
Still, the popular image of the inverted cross as a Satanic symbol - as a mockery of the crucifix - proliferated, especially among rock bands in Hollywood movies. For examples, in the band Coven's debut album Witchcraft Destroys Minds & Reaps Souls (1969), they are prominently wearing inverted cross on their necks in place of crucifixes, and the inverted cross would be incorporated into their logo. Coven would become a major influence on "Black Metal" or "Satanic Metal" - just as Rosemary's Baby (1968), which used an inverted cross in its advertizing materials, would go on to inspire generations of "Satanic" and occult thrillers.