The idea that William Shakespeare was a "closet Catholic" has been stewing for a number of years. I think there is something to this idea inasmuch as Shakespeare's public life is so well documented, but he managed to draw a veil over his private life. Likewise, the ghost in Hamlet is a fairly obvious reference to Purgatory.
Apparently, the Archbishop of Canterbury is in agreement:
When the archbishop of Canterbury recently broke his church’s long silence and acknowledged that William Shakespeare was probably a Catholic, it was a moment of quiet satisfaction for Father Peter Milward, the author who began researching this subject a half century ago.
“I think the archbishop of Canterbury got his ideas from my book,” suggested Father Milward, a soft-spoken, seemingly ageless Jesuit academic who taught English literature at Sophia University in Tokyo and used his off hours to investigate the subject from every angle, producing several key works.
Father Milward is best known for several books: Shakespeare’s Religious Background (1973) and two volumes of Religious Controversies of the Elizabethan Age and the Jacobean Age in 1977 and 1978.
Vice chairman of the Renaissance Institute of Sophia, Father Milward is editor of Renaissance Monographs and the first director of the university library’s Renaissance Centre.
“Shakespeare and the identity of England in the Elizabethan and Jacobean periods has long interested scholars,” said British Benedictine scholar Abbot Aidan Bellenger of Downside Abbey, author of numerous works on Church history. “The weight of opinion has placed Protestantism and Shakespeare in close proximity. Shakespeare studies have thus been shaken up by the gently spoken Jesuit, Father Peter Milward. In a series of thought-provoking and insightful literary studies, he has challenged the orthodoxies of the established Shakespeare scholar and has provided an alternative Shakespeare — profoundly Catholic and truly English.”
“To be a Catholic in Elizabethan England has often been seen as being a stranger in one’s own country,” he said. “Father Milward’s great achievement has been to bring Shakespeare’s Catholicism into the mainstream of national identity. It may be [that] to be truly Catholic in the age of Shakespeare was to be truly English.”