The same as it did with religion: in spite of it.

The scientific revolution was in fact born of occultism. "Science" was just the magic that worked. Francis Bacon was a Thaumaturge, Tycho Brahe was an astrologer, Paracelsus and Dee were sorcerers, alchemists and diviners, Kepler a numerologist and neo-Pythagorean mystic, Newton an alchemist and hermeticist. The theory in the History of Science is that the inability of religion and pious natural philosophy to prevent or solve the horrors of the 14th & 15th centuries, and the gradual breakdown of the Medieval Synthesis (1453-1519) gave rise to "the Faustian impulse" -- the quest for human power over nature. That quest which began in occult studies and experimentation reached its climax in Newton's Principia, after which point Science and Occultism diverged, though they cohabitated in Freemasonry for another century. The witch-hunting craze of the 16th and early 17th centuries was, however, just part of the religious hysteria and fanaticism of the time, all of it born of a world in paradigm collapse. The Medieval world was by no means a benighted, bigoted and superstitious time - at least no more so than any other time, even ours. It was, however, marked and indeed supported by a consistent all-encompassing worldview that was shared by virtually all Europeans. That paradigm began to fracture and eventually shattered under the weight of the Black Death, the Great Schism, the Fall of Constantinople, the Borgia and Medici popes, the advent of "the New Learning" (resulting from Greek Biblical and Patristic texts fleeing out of Byzantium escaping the Turks), direct trade relations with India and the Far East, and the discovery of America. This was something like the existential and cultural equivalent of the meteor strike that killed off the dinosaurs and pulverized the biosphere: in its wake new and often not well-thought out worldviews sprung up all over the place, with people clutching to them for dear life -- and when they came into contact with different worldviews, they often over-reacted against each other. People started seeing threats and demons everywhere. Innocuous or and even utterly trivial points of difference became regarded as fundamental articles of faith vs. intolerable heresy. (Not only were people in the West killing each other over whether the Eucharistic bread and wine transubstantiated into (became in toto) the flesh and blood of Christ or rather just became consubstantial with them (became his flesh and blood while also remaining bread and wine), the Russian Orthodox were killing each other over whether you crossed yourself with 3 fingers or 2!) Indeed, they acted as if their entire world was at stake on every point of doctrine and practice -- and in a way, it was. Their fledgling worldviews/paradigms were that awkward, that sensitive, that un-developed, and that fragile. You might say, none had any natural immunities and mutual predation was driving a very rapid evolution in intellectual, philosophical, theological, and political spheres. By way of comparison, ever deal with a young new "on fire" "born again" convert to anything? Ever see what happens when you put him in the same room (or an internet chat room) with a similar newbie from another creed or school of thought? Compare them to a pair of older, wiser, far more experienced soldiers of their respective faiths, no less convinced of the truth of their respective creeds, and they sit down like two old buddies - one who went Navy and the other who went Army - and have a grand old time talking and razzing each other ... and heartily agreeing over what a bunch of idiots the new recruits are. In the 16th Century you have inquisitions, pogroms, expulsions, wars of religion, and witch-hunts; by the 20th century you had "A priest, a minister, and rabbi walk into a bar ..." and "witches" are characters you find in Oz and Hogwarts.

Alchemy

Because the powers that existed at the time although having come here to escape Religious persecution... Were still ignorant and religious driven and minded people that were superstitious and really dangerous and evil as a result. I believe the Queen/King sent them to put a stop to scientific progress in the States???

Even Christianity coexisted with the scientific method. If Christianity can do it, witchcraft is easy.