Like most English people until well into the twentieth century, Shakespeare was baptized into the Anglican church, but it does not follow that he was himself any more religious than the average Englishman of his time; and the treatment of Jews in The Merchant of Venice is a weak basis for the argument that Shakespeare himself was a devout Christian.
To begin with, there's the obvious fact that devout Christianity is not a prerequisite for antisemitism: Hitler's skepticism toward the church is well attested. So the fact that Shakespeare's play could be considered antisemitic tells us nothing about his Christianity or lack thereof.
Second, there's the example of Shakespeare's contemporary Christopher Marlowe. His The Jew of Malta is far more gleeful in its antisemitism than even The Merchant of Venice. Michael Keefer writes:
Marlowe's Barabas (whose only offense, beyond an arrogant narcissism, has been the greed that motivates him to enclose "Infinite riches in a little room") is similarly cheated by dishonest Christians, who after seizing his property in order to pay the tribute owing to the Turks, keep it even once they've decided to refuse the tribute. The play devolves into a sequence of farcical acts of revenge and cover-up, but the notion that Christians are ethically inferior to Jews remains in circulation: Barabas may outdo in malice the Christians who have robbed him, but he is scarcely their equal in hypocrisy. The Jew of Malta, in short, is antisemitic, but its antisemitism is, at least in part, a means of leveraging a satirical onslaught against Christian mores.
Both Barabas and Shylock further the stereotype of the conniving, greedy Jew, but in Marlowe's play, the Christians are not much better; and in Shakespeare, Shylock too is a victim of Antonio's antisemitism. When asked why he is so eager to enforce the contract against Antonio, Shylock says:
...if it will feed nothing else, it will feed my revenge. He hath disgraced me, and hindered me half a million; laughed at my losses, mocked at my gains, scorned my nation, thwarted my bargains, cooled my friends, heated mine enemies; and what's his reason? I am a Jew. Hath not a Jew eyes? hath not a Jew hands, organs, dimensions, senses, affections, passions? fed with the same food, hurt with the same weapons, subject to the same diseases, healed by the same means, warmed and cooled by the same winter and summer, as a Christian is? If you prick us, do we not bleed? if you tickle us, do we not laugh? if you poison us, do we not die? and if you wrong us, shall we not revenge?
Even as they promulgate antisemitism, both plays also take a critical attitude toward it. The behavior of antisemitic Christians is not treated as justified by virtue of their Christianity or their antagonists' Judaism.
Furthermore, Marlowe's own beliefs demonstrate that writing an antisemitic play is no indication of devout Christianity. He is generally supposed to be an atheist. His sometime roommate Richard Baines, a double agent and former Catholic priest, accused him of being so in a celebrated note, written to and at the behest of one of the members of Queen Elizabeth's cabinet. The note says that with regard to atheistic views:
Marloe doth not only holde them himself, but almost into every company he cometh, perswadeth men to Atheisme, willinge them not to be afrayed of bugbeares and hobgoblins, and utterly scorning both God and his ministers.
If Marlowe could write an antisemitic play while holding atheist views, then we cannot assume that by virtue of writing an antisemitic play, Shakespeare must have been Christian.
To sum up:
- Devout Christianity is not a prerequisite for antisemitism.
- The antisemitism of The Merchant of Venice is not entirely straightforward; the antisemitism of Christians itself also comes under some critical scrutiny in the play.
- Marlowe's example shows that writing an antisemitic play could be compatible with any range of religious views up to and including atheism.
In short, the antisemitism of Shakespeare's play is no evidence for ascribing devoutly Christian beliefs to him.