Shakespeare's views?

Shakespeare himself, as ever, is impossible to pin down. There was certainly a wide range of belief within his audience.

The Bible is unequivocal about the existence of witches*; hence there were very few, if any, who would maintain that witches could not exist*. But writers like Scot show that others held more skeptical attitudes.

There is good evidence that Shakespeare had read Scot; certainly he read Samuel Harsnet's Declaration of Egregious Popish Impostures (1603), for he used many of the names of devils in it in Edgar's "mad" speeches in King Lear.* Harsnet's work is very much indebted to Scot, and is a thorough denunciation of belief in witchcraft.

Pets or "Familiars"?

The Devil was supposed to appear to witches in the form of an animal, a cat, an owl, a mouse, and so on (see Leviticus* 19:31). In the first scene of Macbeth, the three witches respond to their familiars:

First Witch: I come Greymalkin [a grey cat].
Second Witch: Paddock [a toad] calls.
Third Witch [perhaps responding to an owl call]: Anon [at once]!
(1.1.8-9)

Thus an old woman who kept a cat, or whose house was infested with rats, could be accused of having familiars.

Samuel Harsnett's A Declaration of egregious Popish Impostures (1603) is on line.