Christianity took root as an offshoot of Jewish religion at a time when Europe, the Near and Middle East, and Northern Africa were dominated by a variety of religions. Christianity was a monotheistic cult at this period, and largely inherited Jewish ideas about other gods being false. Into the medieval era, this set of beliefs was codified in the idea that "pagan" deities were actually demons or evil spirits, and as Satan gained traction in medieval demonology as "the Adversary" opposed to God, the idea of a unified opposition to the increasingly monolithic Christian church at Rome began to develop.

Which is a long way to say, "Satanism" was not a strong concept until well after the Roman Catholic Church had gained substantial presence and influence as an institution. There were various heresies and "pagan" religions, and some of these were associated with or blamed on Satan, but the degree to which there was ever an actual group or tradition of Satanism in the pre-modern period seems unlikely. When you read accusations of heresy such as the Knights Templar worshipping Baphomet in the inquisition of 1307, that is a combination of propaganda and confirmation bias - if you're bound and determined to find Satanists, anything that looks different is going to be considered Satanic to your inquisitor.

Satanism as an idea fluctuated but gained currency, particularly in literary circles, over the subsequent centuries. There may have been isolated individuals and groups inspired by this literature to form "Satanic" groups, but to what degree that these were actual believers versus poseurs, dilettantes, or conmen is a bit of an open question. Were the Hellfire Clubs of the 1700s actually Satanists? Did La Voisin actually arrange black masses in France in the late 1600s? It becomes really difficult to differentiate fact from fiction, considering the hype involved.

But we can say that the Church of Satan was founded by Anton LaVey in 1966. And this is very significant because the Church of Satan focuses on non-theistic Satanism. That is, they do not actually worship Satan as any kind of god or entity for intercession; they take the spirit of and symbolism of Lucifer as the original rebel and work outwards from that. And unlike the classical idea of Satanism, the Church of Satan is not directly opposed to the organization or existence of Christianity, it's more like a subversive philosophy.

Theistic Satanism has sometimes been practiced by small groups in contemporary times, and because of the nature of the development of religion in the Near East and Middle East, there are some rough parallels.

Yazidism, for example, was often mistaken by pulp writers in the early 20th century as being essentially devil worship. It is a monotheistic religion with ties and parallels to Judaism, Christianity, Islam, Gnosticism, and Manichaeism, except that the Yazidi revere "Tawûsê Melek" ("Melek Taus", "the Peacock Angel"), a bit of a demiurge figure who has parallels with Lucifer as the first among angels. The conflation and confusion of this figure with comparable figures in Christian angelology and demonology has been responsible for a lot of erroneous ideas regarding the nature of Satanism and its prevalence in general, and is part of the widespread discrimination against the Yazidi. As a religion, Yazidism is most definitely not Satanism, but if you're looking at it through a very narrow lens, that's what people have interpreted it as.

Satanism is so specific to Christianity and related religions in that regard it becomes supremely difficult to draw effective parallels with other religions. Many religions don't have clear or absolute delineations between good and evil, much less personifications of them. So it becomes really tricky to apply equivalencies. The idea, unfortunately, has a lot of currency and appeal to audiences that are used to thinking in fairly dualistic terms, which is why in Indiana Jones and the Temple of Doom the Cult of Kali is presented as specifically opposed to "normal" Hindu religion, with Indy actually using a formula that Mola Ram has "betrayed Shiva."

So any equivalent you have to draw, you have to consider the cultural lens you're looking at it from - and in the case of historical sources, the cultural lens they are looking at it from, since very often the religion or sect is extinct in the contemporary period and all we have regarding its beliefs is what was written down by people that were opposed to, or at least alien to, their religion.