Provoked by the question, research into this idea was necessary. Upon completion, one commonality is found (defined by Cambridge Collections Online: Shakespeare Survey Volume 62: "Close Encounters with Shakespeare's Text").
Close encounters with Shakespeare viewed through a post-colonial lens illustrate that culture is hybrid.
Postcolonial theory typically tends to look at how a culture functions under the power of a different culture. While this may sound confusing, it is no more than the examination of a culture who is controlled and influenced by another.
What this means is that Shakespeare's works can be examined through a Postcolonial lens based upon the fact that his background is a blending of two very diverse cultures and/or traditions. Personally, Shakespeare was a practical person. Ironically, the characters in his plays are not. Essentially, his characters contrast his person so greatly that one could state that he and his characters are culturally different. This is where one could apply a Postcolonial lens to his plays.
For example, Lady Macbeth (Macbeth) is very impractical. At one point in the play, she prays to be "unsexed" in order to have the recognized power which men typically possessed. She fails to see ambition in her husband. That said, she prays for the power to be a man. Shakespeare, himself, as a practical person, would recognize the ridiculousness of this.
One other tie to Postcolonialism brought up, in the article mentioned above, is the idea that "long after our own cultural artifacts reveal that binary models are an artificial and inadequate way to understand how people live" people will include the in the idea of "how they live with Shakespeare." This refers to the idea that Shakespeare is a culture of his own. Reading into his works, critics can apply a Postcolonial lens to the texts based upon Shakespeare's place in society as a literaryy institution (or power).