Thank God for the Spanish and Italian Inquisitions (the Popes, too)

      "Clearly, then, popular belief throughout Italy and Iberia, and their attendant islands [(i.e. 'the Western Mediterranean basin' characterized by 'Mediterranean Mildness')], could have assimilated the [fearsome] new [(i.e. early 15th-century)] model of witchcraft [that had originated in the Western Alps], and counter-balancing cultural traits could only have slowed down that assimilation.  Another [mitigating] factor must [therefore] have been at work, and Gunnar Knutsen spotted it in his comparison between Catalonia and Valencia:  in the former, the Spanish Inquisition was much weaker than in the latter, and less able to restrain lay magistrates who responded more avidly to a public fear of witchcraft.  Such restraint was the crucial determinant of result:  in Valencia the girl who confessed to having sex with Satan was sentenced to religious instruction (after a beating), the woman accused of night flight was acquitted, and the would-be witch-finder was punished.  In all the other cases of alleged diabolism cited above, similar moderation was observed and diabolic elements played down by the inquisitors:  the woman who was forced to confess to demonic witchcraft by the Italian friar was then released on the orders of his superior.  General studies of the history of the respective inquisitions reveal a gradual formulation of central policy that made such outcomes at first possible and then mandatory.
     "In 1542 a central tribunal was established in Rome to oversee local Italian inquisitions, and by the 1580s this was advising caution in local trials of witches and enforcing it on some.  In 1575 Pope Gregory XIII ruled that nobody could be arrested simply because of a denunciation by somebody already under trial for witchcraft, while in 1594 Pope Clement VIII banished a southern Italian bishop whom he thought had prosecuted it too recklessly.  Around 1600 the tribunal accepted a protocol which was sent out to most Italian inquisitors from the 1610s:  all alleged deaths from witchcraft were to be investigated by medical experts operating under oath; suspects were to be held in different cells to prevent them from mutually reinforcing their fantasies; and investigators were to avoid any leading questions, identify local hatreds operating in accusations, and consider only objective evidence.  This made convictions for witchcraft practically impossible, and after 1630 papal authority effectively ended witch trials in the Italian peninsula.
     "A parallel process occurred in Spain, where from 1525 the Supreme Council of the national [i.e. the Spanish] Inquisition began to reduce death sentences imposed on suspected witches by its local representatives, accusing the latter of excessive credulity and use of torture to force confessions.  In 1526 it anticipated the later papal decree by decades, ordering that nobody should be arrested simply on the testimony of somebody already accused of witchcraft.  It also sought to take over itself the cases of those formally charged with witchcraft who pleaded innocence.  The last execution of somebody for witchcraft by a member of the Inquisition in Aragon was in 1535, and the last in Catalonia in 1548.  Trials persisted in Navarre, and in 1609 a serious witch-hunt on the French side of the border spilled over into that province, and produced a major panic, with almost two thousand accusations.  The first inquisitors to deal with them were persuaded of the reality of some, and burned six people.  Subsequently, however, the Supreme Council sent out a more scrupulous representative, Alonso de Salazar y Frias, who became convinced of the patent falsity of most confessions, and the impossibility of clear proof in the case of the remainder.  His report convinced his superiors, who were also shocked by the expense of the investigation.  Thereafter they adopted a code of rules for trials of alleged satanic witches which demanded such stringent proofs that it rendered convictions virtually impossible.  Witch-hunting was now confined to those parts of north-eastern Spain, especially Catalonia, where the authority of the [Spanish] Inquisition was weakest and trials could be conducted by secular courts with relative freedom.  Even there, however, the inquisitors did their best to halt the proceedings, reinforced by royal authority from 1620, and by the end of the 1620s Spain was apparently free of trials for diabolic witchcraft.
     "The great influence of the Papacy and the Spanish upon the western Mediterranean lands in general explains why the other territories in the region followed the same trajectory in the same period.  The new oversight and professionalism injected into the inquisitorial process by the foundation of central supervisory bodies seems in itself to have engendered a more rigorous and sceptical attitude towards accusations of demonic witchcraft, and a growing disposition to view even those people who confessed to dealings with the Devil as deluded and in need of redemption.  This change then became a factor in regional power politics, as interventions to prevent credulous and destructive witch-hunting enabled the central tribunals to enforce their authority more effectively over the localities.  Eventually a cautious attitude to accusations of witchcraft, and a programme of correction and not extermination for those convicted of attempting to work magic, became a matter of ethnic identity.  Seventeenth-century Italians, in particular, could be surprised and horrified by the huge body counts being stacked up by witch-hunts in Northern Europe.  The Mediterranean inquisitions remained forbiddingly effective machines for the persecution of magical practices, and even moderate punishments such as imprisonment, flogging and public penance would have been traumatic for those who suffered them.  None the less, they rescued a region representing about a quarter of Europe from the most concentrated and deadly period of the early modern witch trials.  They seem to have done so, moreover, because of political and ideological developments among the religious elite, in which popular beliefs played only a supporting role, in certain places, and not a decisive one."

     Ronald Hutton, The witch:  a history of fear, from ancient times to the present (New Haven, CT:  Yale University Press, 2017), chap. 7, subsection on "Mediterranean mildness."  (I am citing chapters rather than pages until I can insert the latter with the book (rather than just the differentially paginated browser-based e-book) in hand.)
     Hutton gives here what his review of the scholarship of his fellow specialists indicates was the reason for the approximately 500 executions in this area between 1560 and 1640 by comparison with the "between forty and sixty [(most likely less than fifty)] thousand people . . . legally put to death for the alleged crime of witchcraft" between 1424 and 1782 across Europe (and especially Northern Europe) as a whole, the former despite the fact that 1560-1640 was precisely "the period in which the regional inquisitions that defended the purity of the Roman Catholic religion in the Western Mediterranean basin, and which represented some of the most formidably efficient investigative and punitive machines in Europe, launched an attack on magical practices of all kinds."
     What he says at the end of chap. 7 here about the role played by "popular beliefs" in witch trials of the 15th-18th (or 16th-17th) centuries, whether medieval or even in a few cases ancient (that it was minor), is also what he says in the following paragraphs about "the core [northern] area of the early modern witch trials, where [by contrast] the majority of their victims [(the majority of those tried)] perished:  the German-speaking lands, the French-speaking parts of the Rhine and Moselle basis to their west and Poland to their east" (and presumably (?) other regions even further north, for example the British Isles and Scandinavia):  that they, too, were dominated in a top-down fashion by the new and largely unprecedented conception of witchcraft that arose out of the Western Alps in the 1420s (the pact with Satan or his demons, the Witches' Sabbath, the supposedly organized religion of Satan worship, etc.), and not by popular local traditions, however—as in the case of an inconsistent smattering of the motifs—ancient, so that the mentality responsible for the killing was almost entirely modern, and the influence (from the elites—until they caught up with those of the Western Mediterranean—downwards), mostly unidirectional.  The trials "were propelled and dominated . . . by a new, almost pan-European concept of witchcraft propagated by elites and accepted into general culture."
     I.e., it did it not arise out of an ancient or even medieval Satan-worship organically from below, but was a novum of a comparatively short duration:

modern historians completely reject the literal reality of that cult, however much they may attempt to understand and explain belief in it.  In this they are simply following the path laid out by early modern scholarly opinion itself, which came, first in practice and then in theory, to abandon that belief.  After all, medieval Europeans did not have it either, until the fifteenth century, and in long historical perspective it was a relatively short-lived phenomenon. . . .  This is an area in which no academic investigator ever goes native" or even "agnostic," regardless of "whether there [ever] were any actual would-be satanic witches in early modern Europe."  (Though "all the professional research of the past half century[, unwilling to step 'over the boundaries of current scientific knowledge',] seems to unite behind the conclusion that there were not, and that all of the witches’ assemblies described in the records were illusory [(the inquisitor Salazar:  "'the witches are not to be believed'")].  Furthermore, . . . there is an equal consensus that accounts of those assemblies were not mistaken or distorted portraits of some other religious tradition, such as a pagan one:  they just never happened.

But keep reading to the end of chap. 7 and beyond.  What follows at just the end of chap. 7 alone is quite nuanced.)
     As for the period after the witch-hunts of the fourth century, for which latter it isn't at all clear that Christianity was in any decisive respect responsible, there is this summary of chap. 6 (which, with Prof. Hutton's written concurrence, corrects the inadvertent transposition of the terms "encourage" and "discourage"):

What seems to be especially significant in th[e surviving] records is the part played by churchmen.  As said, they regularly and vehemently condemned all or most kinds of magic as demonically inspired and assisted, and none seems to have argued against a belief in witchcraft; indeed, the most influential theologian of the central Middle Ages, Thomas Aquinas, ruled firmly that the Christian faith proclaimed that to dispute the existence and effectiveness of harmful magic was to deny the reality of demons.  On the other hand, they did not develop any theology that demanded and encouraged the hunting of witches either, and, in practice, seem to have acted more frequently to [discourage] than to [encourage] it before 1300. . . . 

. . . Churchmen between 500 and 1300 were also generally consistent in condemning as illusions and superstitutions some widely held popular beliefs which would, had they taken them literally instead, have encouraged witch-hunting. . . .  [The] belief . . . that . . . night-roaming cannibal women who attacked sleeping people, children or adults, and consumed their organs[,] . . . embodied in the earliest surviving Germanic law code, was outlawed in subsequent codes as the effect of Christianity (and perhaps of educated Roman opinion, which had questioned the reality of the strix demon from pagan times) was felt.  Early medieval sermons and penitentials continued to condemn belief in such figures as a fiction.  Thus it can be suggested that early and high medieval churchmen both believed in the existence of magicians—and indeed this was beyond doubt as there were always plenty of people offering magical services, and also probably some who did attempt to use magic to harm enemies—and the need to stop them; and yet operated in many ways to reduce the likelihood of frequent and large-scale witch-hunting. 

. . . It may be that, once again, ideological factors were more significant than functional factors in producing a low and intermittent rate of persecution of presumed witches.  After all, exactly the same period, of the twelfth and thirteenth centuries, saw what has been called ‘the formation of a persecuting society’ in Europe, as its peoples turned upon Jews and homosexuals with a new hostility and introduced ever more rigorous measures and structures to deal with a new problem of widespread and mass Christian heresy.  The witch-figure, however, did not get caught up in these developments.