In Merchant of Venice the main driver of the plot is a jew by the name of Shylock. The short version is that he lends money and then goes to court when the person he's lent money to can't pay. Antonio, the debtor, has promised a pound of his own flesh. Shylock pursues this beyond what is sane and is ruined for his obsession. Are Shakespeare's personal feelings on Shylock's religion known? To the society Shakespeare lived in would Shylock's religion been another flaw added to the list? Was Shylock's monologue showing Jews as equals to Christians ("if you prick us, do we not bleed?") seen as some radical view at the time or would there have been a discussion about the issue?
I'm not really concerned with how Jews were treated, or with what Shakespeare thought specifically, but rather what the history of political sentiment on the issue of antisemitism. Would some of them be disgusted when a Christian in the play spits on Shylock? What was the state of discourse on the subject at the time of the play's writing?
Shylock's monologue showing Jews as equals to Christians ("if you prick us, do we not bleed?")
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, heal'd by the same means,
warm'd and cool'd 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?
If we are like you in the rest, we will resemble you in that.
If a Jew wrong a Christian, what is his humility?
Revenge. If a Christian wrong a Jew, what should his
sufferance be by Christian example? Why, revenge.
The villainy you teach me, I will execute,
and it shall go hard but I will better the instruction.
(Act III, scene I)
On a lit-crit rather than a historical note, it's important to remember that the speech isn't an impassioned plea for equal treatment but rather a villain's self-justification; "you Christians condemn me for taking revenge, but I learned that off you, and the way you treat us. We're not so different, you and I..."
For an exact answer you'll need an expert on the history of anti-Semitism. I'll try my best to provide some answer as far as the Shakespearean side goes.
Are Shakespeare's personal feelings on Shylock's religion known?
No, there is no such data on Shakespeare's private opinions. All we have when it comes to these matters is what can (or cannot) be derived from the text of the plays.
To the society Shakespeare lived in would Shylock's religion been another flaw added to the list?
This is not exactly my cup of tea so best I can do is share with you what I can find on the subject in my Penguins edition of the play (by Peter Holland):
Jews had been expulsed from England as far back as 1290. But there were Jews in England in Shakespeare's day, who had publicly converted to Christianity, but some may very well have secretly maintained their original religion. In general the public perception and theatrical depiction of Jews was extremely negative. Holland gives Robert Wilson's The Three Ladies of London as an example of a play that included a good and generous Jew. But the majority of Jews on the Elizabethan stage were villains of various levels of severity.
Would some of them be disgusted when a Christian in the play spits on Shylock?
I'll just add here, before going into the more complicated part below, there is no literal spitting on Shylock in Shakespeare's play. Shylock says Antonio spat on him, but we never see it happen, there's a leeway for the audience to decide for themselves whether this really happened or if Shylock is exaggerating/imagining things. Some performances do include this spitting, notably Al Pacino's 2004 movie (Youtube, NSFW), but I know of no indication this would've been part of the Elizabethan performance.
Was Shylock's monologue showing Jews as equals to Christians ("if you prick us, do we not bleed?") seen as some radical view at the time or would there have been a discussion about the issue?
Now this is the real issue of course. But as Brickie78 pointed out, you're already somewhat jumping to conclusions when you decide the "Hath not a Jew eyes?" speech is a plea for Jews as equals to Christians. I would note that not long after that speech, Shylock is forced to convert to Christianity. I could easily offer the interpretation that Shylock's speech identifies himself as a fallen man, who is in need of Christ's deliverance.
The issue of Shylock's character, and to what extant Merchant of Venice is innately anti-Semitic, is one that I've seen scholars argue to and fro about without a clear cut conclusion. The only thing I'd want to say is that Shakespeare lived in an era when religious persecution was common. While his own religion is a matter of debate, it is generally accepted that his father was a secret Catholic. And the persecution of protestants under queen Mary would've been fresh in the minds of many of Shakespeare's older contemporaries. In "The Merchant of Venice and Pressured Conversions in Shakespeare's World", Marianne Novy argues Shakespeare might've deliberately been trying to equate the persecuted Jews to persecuted Christians as a way of advocating religious tolerance. But it's not something that has been definitely proven either way.