Mathematics and astrology. Nearly everyone believed in astrology, that the stars held the secrets to their character and future. This was not seen as superstition. For example Dr. Dee was the Court astrologer. Several crowned heads of Europe asked him to join their Court. The study of mathematics was viewed as an esoteric art imputing to the practitioner mystical powers. It was regarded with suspicion by some. It is reported by the 17th century antiquarian John Aubrey that the Tudor authorities had 'burned Mathematical books for Conjuring books. The term calculating (sometimes corrupted to calculing) was synonymous with conjuration. Pythagorus himself was considered a magician. A biography of John Dee explains this well : The Queen's Conjuror : the Life and Magic of Dr. Dee - Benjamin Woolley. I'll leave it to someone else to speak to witchcraft and wise women.

John Dee is not a specialty of mine, but in general, alchemy and astrology were considered in line with other "practical sciences" (like mathematics and engineering) up until the late "Scientific Revolution." That is, they weren't magic or witchcraft, they were "naturalistic" understandings of the supernatural (God). They were also, in the European context, closely aligned with imagined ideas about Judeo-Christianity, going back to Solomon or Moses in the alchemists' bizarre (but widely-held) understanding of their craft. They saw themselves as understanding the nature of the universe, as hidden by God in scripture and the fabric of the cosmos itself.

The people who practices such things were often of a rather higher class as well, which doesn't hurt. These are often people who, if not actual courtiers themselves, then served courtiers.

This doesn't mean it was universally tolerated. Henry IV passed a law banning alchemy, for example, though it was practiced both under some official capabilities and in secret until Charles II (a closet alchemist) repealed the law (at the admonition of Robert Boyle). Henry VIII apparently attempted to use alchemists at the Royal Mint, but Elizabeth only approved a few official alchemists.

So while the fortunes of alchemists could wax and wane, and there were certainly those who would have thought the whole thing stunk of black magic, on the whole alchemists and astrologers were pretty well tolerated as "experts" of a practical sort. Today we see them as pseudoscientists at best, charlatans and "magicians" at worst, but the boundaries between the "real" sciences and the "pseudo" sciences were very porous up until the late 18th century or so. (Isaac Newton and Robert Boyle were both alchemists; the generation after them spent more time policing the boundary between alchemy and chemistry.)

We can contrast this with the idea of witches, which are people in this mindset who have made a pact with Satan to do bad things to no particular end. These are outsiders, these are people who are not part of the state hierarchy, they are seen as dabbling with truly supernatural forces, not appealing to special knowledge from God. So the whole thing would be framed very differently.

It is worth noting that John Dee did actively work to ensure that his particular investigations (his conversations with angels) were not construed as cavorting with demons. Deborah Harkness examines in John Dee's Conversations with Angels how he positioned himself as a critical investigator of the book of nature. John Dee was well aware of the dangers of his practice---that is, there was the belief that any kind of meddling in the "supernatural" always held risk of exposing oneself to demonic influence.

Johannes Trithemius' (a fifteenth century Benedictine, whose interests in the occult were not unlike Dee's) attempts to develop a occult study within the bounds of Christian practice. He was heavily criticized by opponents on the grounds that the human intellect is not sufficiently aware to determine of otherworldly beings were malicious or angelic. Trithemius disagreed with this objection to the study of the occult, and argued that a person with sufficient will could resist demonic influence. For Trithemius, demons only offer false knowledge---that is, they employed their own knowledge of the occult to do the deeds of men, tricking them in the process to giving up their soul or their faithfulness to Christ. Trithemius instead wanted to study and gain true knowledge of the occult, so as to better understand (and master) the forces linking earth and the superior spheres of heaven. (see Brann, Trithemius and Magical Theology for more on Trithemius.)

Dee's solution, in part, to problem that faced Trithemius was to recast his activities not as magic, but as a natural attempt to make contact between this earthly sphere and that sphere in which the angels reside. Dee was not "conjuring" spirits so as to have them perform deeds for him (as Trithemius would argue, is not gaining genuine knowledge), but instead using conventional religious practices (prayer, a scryer, a "lens" stone for cosmic rays, etc) to communicate. In the broader context of his century, Dee believed that he was participating in a necessary activity of consulting with the angels before Armageddon. The notion that the end of time was upon the Christian world was not uncommon, and so both the urgency for his activity and the practices he did were within conventional belief.

In contrast, witches were conceived as active servants to the devil, who hold regular communion with demons, and were typically marginalized members of the community. Rarely were witches or sorcerers publicly visible members of upper class(es). And there is probably good reason to believe that in all the English intolerance for witches, very few of the people punished were actually participating in diabolical practices. In fact, again, the activities of being a witch were most widely believed to be the employment of demons to do things. And Dee was not trying to employ his angels to do anything more than gather knowledge of the end of days and the role Christians like him would play.