Lady Macbeth of the play Macbeth has often been seen as one of Shakespeare's strongest women; in fact, some may see her as an early feminist. Why?

Consider this famous speech of Lady Macbeth's.  It is some of the best evidence that she held "feminist" beliefs: 

Come, you spirits
That tend on mortal thoughts, unsex me here;
And fill me, from the crown to the toe, top-full
Of direst cruelty! make thick my blood,
Stop up the access and passage to remorse,
That no compunctious visitings of nature
Shake my fell purpose, nor keep peace between
The effect and it! Come to my woman's breasts,
And take my milk for gall, your murdering ministers,
Wherever in your sightless substances
You wait on nature's mischief!

Much of the feminist movement has been motivated by a desire for equality.  Women wanted to be considered just as capable of men as doing every job they did - whether that be the job of voting, holding political office, or performing certain sports.  Here, Lady Macbeth is specifically asking the universe to "unsex" her.  She wants her womanly characteristics taken away so that she can perform the duties that society says is a "man's job".