It wasn't really necessary, but I googled "Shakespeare and Christianity" and was amused to see the first entry arguing for a connection, the second against this, the third by Aldous Huxley (!) and Wikipedia hemming and hawing at fourth. Not that I can add much to the general conclusions, despite my finding a great heap of previously undetected Christian references in Shakespeare, particularly in Troilus and Cressida (a 1609 play containing a most curious allusion to a "creative addition" to the 1611 King James Bible, among other Christian things). No, Shakespeare's religion, like his politics, remains an enigma to unriddle.
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But of course I had to check the Aldous Huxley, and I'm happy to say it jives with my impression of Shakespeare as deeply steeped in a sense of religiosity, often expressed via the Christianity that was his milieu (and what do you bet it was precisely this religious feeling that captured Bob Dylan?) Nevertheless, I must quibble with one of Huxley's examples, the report of Falstaff's death by Mistress Quickly, from Henry V. As Huxley quotes it:
HOSTESS: Nay, sure, he's not in hell: he's in Arthur's bosom, if ever man went to Arthur's bosom. 'A made a finer end, and went away, an it had been any christom child; 'a parted ev'n just between twelve and one, ev'n at the turning o' th' tide: for after I saw him fumble with the sheets and play with flowers, and smile upon his fingers' ends, I knew there was but one way; for his nose was as sharp as a pen, and 'a babbled of green fields. "How now, Sir John!" quoth I, "what, man! be o'good cheer." So 'a cried out "God, God, God!" three or four times. Now I, to comfort him, bid him 'a should not think of God; I hoped there was no need to trouble himself with any such thoughts yet.
This has two errors: first it isn't a plural "fingers' ends" but a singular "finger's end" as the 1623 Folio has it; no trivial matter, for it (and Abraham's/Arthur's bosom) mark an allusion to the biblical story of Lazarus and Dives, an allusion that greatly clarifies the parallel relationship between Falstaff and King Henry, and ultimately condemns King Henry. But that is a longer story with much additional evidence.
The second error is not quite so serious, indeed it's merely a repeat of the standard (for three centuries) emendation of the Folio's clearly incorrect "his nose was as sharp as a pen, and a table of green fields" (sic) to the intelligible "babbled of green fields." Again, however, the "table" marks a biblical allusion, and it can be retained by recreating the correct text as "and 'a talked of a table of green fields" (my reconstruction, ahem!)
But maybe the most important thing here is truly masterful way Shakespeare accentuates pathos with a touch of humor. A great soul indeed.