Why was witchcraft banned or illegal at the time of Shakespeare or during the Elizabethan Era?

The last accused witch was executed in England in 1682,
almost eighty years after the death of Elizabeth; however during her reign, trials and
convictions for witchcraft had declined dramatically. The reason had little to do with
Elizabeth, but rather was due to the influence of more modern thinking about causes and
events. Supernatural explanations were no longer accepted on face
value.

Witchcraft trials in Europe expanded after Pope
Innocent III believed that witches had caused him to become impotent. As a result, he
issued a Papal Bull which read in part:

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It has indeed lately come to Our ears, not
without afflicting Us with bitter sorrow, that in some parts of Northern Germany, as
well as in the provinces, townships, territories, districts, and dioceses of Mainz,
Cologne, Tréves, Salzburg, and Bremen, many persons of both sexes, unmindful of their
own salvation and straying from the Catholic Faith, have abandoned themselves to devils,
incubi and succubi, and by their incantations, spells, conjurations, and other accursed
charms and crafts, enormities and horrid offences...they blasphemously renounce that
Faith which is theirs by the Sacrament of Baptism, and at the instigation of the Enemy
of Mankind they do not shrink from committing and perpetrating the foulest abominations
and filthiest excesses to the deadly peril of their own souls, whereby they outrage the
Divine Majesty and are a cause of scandal and danger to very
many.

Those primarily accused
were women, who were considered the source of all evil (the word derives from "Eve," who
was first tempted by the Serpent) and were generally keepers of oral tradition. Large
numbers were hanged or burned at the stake, generally after having confessed under
torture.

Over time, the more educated began seeking natural
rather than supernatural explanations for events. The fact that confessions were
accepted under torture made them more suspect; and it was believed that secular courts
should not meddle in religious matters. Cyrano de Bergerac once
commented:

No
I do not believe in witches, even though several important people do not agree with me,
and I defer to no man’s authority unless it is accompanied by reason and comes from
God.

Elizabeth I was much
more accommodating than had been her half sister, Mary I. Executions and burnings for
religious matters declined dramatically under her reign, including those for witchcraft.
The decline of witchcraft trials was part of her more humane method of rule, in which
she sought to compromise with all religious groups. Still, the timing for the end of
witchcraft is largely coincidental to her reign.