I would like to add just a little to the views of Hal Colebach on Shakespeare's religious affiliation. Unfortunately I cannot give names, dates, etc, as concrete proof.
Many years ago, when I was studying to become a teacher, during one lecture the matter came up of Shakespeare and his ties with Lancashire - the college at which I was studying being in Lancashire. The lecturer said that there is in existence a book with the various stories of Hamlet, King Lear, etc, and that this book had annotations, in what was claimed to be Shakespeare's handwriting. Thus it was the source he used for his plays.
This book belonged to one of the landed gentry of Lancashire (it may have been the Blundells, but I cannot remember that) and it was reasonable to suppose that Shakespeare spent quite some time with a band of travelling actors, going from country house to country house in Lancashire. It would suggest that he wrote his plays for those players while he was in Lancashire.
Now, the landed gentry in Lancashire (especially the Blundells) were almost entirely, solidly Catholic, despite Elizabeth's persecution. This would mean then that Shakespeare was well-received and moved about quite freely and happily in Catholic Lancashire.
I am aware that this "proves" nothing but it strongly suggests, if true, that Shakespeare was well- versed in Catholic beliefs and practices and may even have been one himself.
JOHN A. RAYNER