Short answers, pulled from the story.
William Shakespeare's known religious affiliation was that of a conforming member of the established Church of England. He and his wife were buried in the church chancel where a monument included a half-figure bust set into the north wall.
Elizabethan Religious Settlement severed Church of England from Roman Catholic Church five years before Shakespeare's birth in 1559. This event placed extreme pressure on English Catholics to accept practices of new church and made illegal any service not found in Book of Common Prayer including Roman Catholic Mass.
Strongest evidence came from a tract professing secret Catholicism signed by John Shakespeare father of poet. New research attributes this tract to William's sister Joan who lived 1569-1646 making genuine copy possible.
William Shakespeare and his wife were buried in the church chancel where a monument included a half-figure bust set into the north wall. His brother Edmund died in London and was buried in St Saviour's in Southwark with a forenoone knell of the great bell.
Scholars speculate that William Shakespeare spent lost years 1585-1592 working under Catholic patronage due to connections through employment and education. These connections form basis for many scholarly arguments about hidden religious affiliations during crucial early career phase.