As to Shakespeare being a crypto-Catholic:
In its favour:
He wrote Falstaff as a satire of the Lollard Oldcastle, who was much revered in Protestant circles.
Many of his works have catholic elements, such as Hamlet's father in purgatory.
His family has some Catholic ties and he was possibly married by a vicar, who turned out to be a hidden priest.
Against it:
Certain plays are explicitly Protestant, such as Henry VIII.
He spent his entire life as a conformist Protestant and was never suspected of Catholic sympathies.
His will is phrased in a Protestant manner, even incorporating Protestant formulae like Sola Christus.
Some have read anti-Catholic sentiment in some of his sonnets, but it is not patently so.
So you can debate if you want. I think the Protestant stronger, and that he merely wrote from within the shared Catholic heritage of Christendom. There is certainly some merit to such allegations though, but they will always remain speculative.