Not exactly racist, but certainly nationalistic. Shakespeare has few good words for his countrymen in Scotland.
'If that you will France win,
Then with Scotland first begin:'
For once the eagle England being in prey,
To her unguarded nest the weasel Scot
Comes sneaking and so sucks her princely eggs,
-Henry V, Act I, sc. ii.
Calling all of Scotland opportunistic weasels might seem inflammatory in today's society. But it's nothing compared to what his contemporary Edmund Spenser wrote in A View of the Present State of Ireland.
"The pamphlet argued that Ireland would never be totally 'pacified' by the English until its indigenous language and customs had been destroyed, if necessary by violence. Spenser recommended scorched earth tactics, such as he had seen used in the Desmond Rebellions, to create famine."
- Wikipedia
Shakespeare's insults seem positively mild in comparison, though they may be said to spring from the same source. This is just the sort of views that they had, completely common and banal. It was a society full of a sort of casual racism and factional bigotry that was just accepted gratis. Genius that he was, I don't think it would have occurred to Shakespeare to treat the subject of race relations or religious orthodoxy ironically, and so you get the usual cast of poisonous cozening Jews, fiendish Muslims, and unfaithful Catholics in his plays as everyone else of his time wrote. Take Christopher Marlowe for example:
BARABAS. As for myself, I walk abroad o' nights,
And kill sick people groaning under walls:
Sometimes I go about and poison wells;
And now and then, to cherish Christian thieves,
I am content to lose some of my crowns,
That I may, walking in my gallery,
See 'em go pinion'd along by my door.
Being young, I studied physic, and began
To practice first upon the Italian;
There I enrich'd the priests with burials,
And always kept the sexton's arms in ure<80>
With digging graves and ringing dead men's knells:
And, after that, was I an engineer,
And in the wars 'twixt France and Germany,
Under pretence of helping Charles the Fifth,
Slew friend and enemy with my stratagems:
Then, after that, was I an usurer,
And with extorting, cozening, forfeiting,
And tricks belonging unto brokery,
I fill'd the gaols with bankrupts in a year,
And with young orphans planted hospitals;
And every moon made some or other mad,
And now and then one hang himself for grief,
Pinning upon his breast a long great scroll
How I with interest tormented him.
But mark how I am blest for plaguing them;--
I have as much coin as will buy the town.
But tell me now, how hast thou spent thy time?
ITHAMORE. Faith, master,
In setting Christian villages on fire,
Chaining of eunuchs, binding galley-slaves.
One time I was an hostler in an inn,
And in the night-time secretly would I steal
To travellers' chambers, and there cut their throats:
Once at Jerusalem, where the pilgrims kneel'd,
I strewed powder on the marble stones,
And therewithal their knees would rankle so,
That I have laugh'd a-good<81> to see the cripples
Go limping home to Christendom on stilts.
-The Jew of Malta, Act II, sc. iii
Here you have both the prototypical evil Jew and the evil Muslim. When Shakespeare re-uses this speech in his own play Titus Andronicus, it's to paint Aaron as your usual black skinned villain:
LUCIUS
Art thou not sorry for these heinous deeds?
AARON
Ay, that I had not done a thousand more.
Even now I curse the day--and yet, I think,
Few come within the compass of my curse,--
Wherein I did not some notorious ill,
As kill a man, or else devise his death,
Ravish a maid, or plot the way to do it,
Accuse some innocent and forswear myself,
Set deadly enmity between two friends,
Make poor men's cattle break their necks;
Set fire on barns and hay-stacks in the night,
And bid the owners quench them with their tears.
Oft have I digg'd up dead men from their graves,
And set them upright at their dear friends' doors,
Even when their sorrows almost were forgot;
And on their skins, as on the bark of trees,
Have with my knife carved in Roman letters,
'Let not your sorrow die, though I am dead.'
Tut, I have done a thousand dreadful things
As willingly as one would kill a fly,
And nothing grieves me heartily indeed
But that I cannot do ten thousand more.
-Titus Andronicus, Act V, sc. i
I think it's safe to say that racism, and regionalism, and other isms of that ilk, were systemic to all English literature of the time. They are shown either in conversation, or in the various roles given to minorities on the stage, and Shakespeare was not above it.

