The depiction of attitudes toward interracial marriage in the play itself is a decent illustration of contemporary English ideas regarding blackness, but also of contemporary English ideas regarding Italian women. (I won't get into the argument about whether Othello is supposed to be "a tawny moor" or a dark-skinned black man for staging purposes -- it strikes me as mostly product of later 18th and 19th century anxieties about miscegenation and the ugliness of blackness, and the characters of the play themselves don't make much of a difference between the two if they see one. Characters speak of Othello's black face and "sooty bosom" rather than stressing an intermediate hue.) In addition to sundry mentions of "blackamoors", "Moors", and "Ethiops", Shakespeare deals with other proposed interracial unions between black men and white women in The Merchant of Venice, with the Prince of Morocco who comes to Venice to pursue marriage with Portia, and in Titus Andronicus between Aaron the Moor and Tamora. Both unions are unhappy, but for different reasons; Aaron the Moor is a rather tragic villain, almost in a Christopher Marlowe vein, and the Prince of Morocco (explicitly textually described as a tawny Moor) is no villain at all -- perhaps pompous but inoffensive. He says in his introduction:

Mislike me not for my complexion,

The shadowed livery of the burnished sun,

To whom I am a neighbor and near bred.

Bring me the fairest creature northward born,

Where Phoebus’ fire scarce thaws the icicles,

And let us make incision for your love

To prove whose blood is reddest, his or mine.

I tell thee, lady, this aspect of mine

Hath feared the valiant; by my love I swear

The best regarded virgins of our clime

Have loved it too. I would not change this hue

Except to steal your thoughts, my gentle queen.

(Merchant of Venice, 2.1)

He's unambiguously princely and unlike Othello, has no especial self-loathing qualities -- his folly is paying too much attention to exteriors, choosing the golden casket instead of the leaden one in the belief that its exterior is an echo of Portia's nobility and beauty. Portia's own reaction to the Prince of Morocco and his complexion is ambivalent to say the least:

A gentle riddance! Draw the curtains, go.

Let all of his complexion choose me so.

(Merchant of Venice, 2.8)

But the Prince of Morocco is hardly dastardly, especially when you compare him to, say, Shylock. In Titus Andronicus, however, Aaron the Moor (with his "fleece of wooly hair" and "his soul black like his face") is Tamora's henchman and lover; other characters treat his race like a stain on Tamora's nobility, "blackening" her honor, and when by chance he begets a child with her, becomes more or less that child's only defender:

NURSE A joyless, dismal, black, and sorrowful issue!

Here is the babe, as loathsome as a toad

Amongst the fair-faced breeders of our clime.

The Empress sends it thee, thy stamp, thy seal,

And bids thee christen it with thy dagger’s point.

AARON Zounds, you whore, is black so base a hue?

[To the baby.] Sweet blowse, you are a beauteous blossom, sure.

DEMETRIUS Villain, what hast thou done?

AARON That which thou canst not undo.

CHIRON Thou hast undone our mother.

AARON Villain, I have done thy mother.

(Titus Andronicus, 4.2)

Aaron is a somewhat sympathetic villain in a Marlovian kind of way, stigmatized by his blackness like Edmund in King Lear is stigmatized by his illegitimacy, and this subplot in particular is hard for me not to feel sympathy for both father and child. But the language used to describe Aaron's blackness as well as his child's is starkly negative, playing on moral blackness as a parallel to physical blackness, and even Tamora herself wants to kill their offspring. Interracial marriages and conjunctions are not unthinkable on the Early Modern English stage, but they're not crowd-pleasers either.

Black men and women were both present in Elizabethan England, particularly in London, and interracial marriages took place there -- there were no legal strictures or social norms to prohibit them, 1590s London was not 1950s Alabama in this respect, and there was no outcry at the depiction of such a marriage on stage. (Would it have been different if Othello were a play with a happy ending for the two lovers, I don't know. Queen Elizabeth I had thorny attitudes toward England's black residents, at one time calling for their expulsion, but by the time Othello premiered she was dead and buried.) These interracial marriages resulted in mixed-race offspring as well as illegitimate ones, and these mixed-race individuals might go down in baptismal registers with their black parent's race noted down as if it were as identifying as a surname -- the offspring of one George Smith went down in the registers of All Saints Church as "George, ye sonne of George, a blackamoore" and "Elizabeth, the daughter of George the Blackamoore". Black people were not exclusively exotics in Elizabethan and Jacobean England; indeed they may have been in the audiences for these plays. But popular stereotypes of blackness were negative and lended themselves to dramatization on the stage anyway -- black characters appeared in Elizabethan and Jacobean drama, and references to black skin pop up with negative connotations to contrast the corresponding idealization of "fair" whiteness. Blackness on the Elizabethan and Jacobean stage is perilously close to devilishness, dirtiness, and difference, not just racially.

In the case of Othello, the double stereotype central to the play's conflict is both that black men are lascivious and that black men are ugly-- black men desire to despoil white women, but no normal white woman would ever desire to wed or copulate with a black man. It's the former that Iago brings out to play on Othello's father-in-law Brabantio, among others, coupled with the idea of black people as sorcerous and treacherous devils -- Othello is called a stranger and a barbarian, and the repeated invocation of witchcraft and spells to explain Othello's seeming hold over a beautiful white woman makes him out in the eyes of white Venetians to be more like Caliban than like Aaron the Moor. But it's the latter racist trope about the ugliness of blackness that Iago uses against Othello himself, targeting his insecurities regarding his own racial difference from his fellow military men and from his bride. What kind of (white) woman could possibly desire a black man? What kind of depraved sexual adventuress would not only accept the favors of a black man but pursue them? Therefore there must be something sexually wrong with Desdemona to accept Othello's attentions.

(Here I'd like to add that Desdemona is not a white English woman -- she's a white Venetian woman, a young beauty from a city marked in the English imagination by associations with luxury, sexual license, and treachery. In fact, though the play is performed in England, none of these characters are English, and Shakespeare and his contemporaries' depictions of Italians as especially hot-blooded, lascivious, and intolerant seem relevant here, not just Othello's own intolerance of his wife's perceived adultery but also the racist outrage Desdemona and Othello's elopement provokes. The lustful freeness of Italian women is a subtext that stokes the fire of Othello's jealousy, and a subtext that is recognizable from other Early Modern drama.)

But Othello himself is not lascivious, and Desdemona is not an insatiable Venetian harlot -- though Othello is jealous, he is not marked by unseemly lust or physical grossness except in the eyes of other characters, and there's little to suggest his relationship with Desdemona was unhappy before Iago's machinations. Othello is distinguished by noble qualities -- his intelligence and valor in war have made him trusted and distinguished even by the same people who excoriate his blackness -- and I see no reason to doubt that Desdemona's attraction to him is textually meant to be read as anything other than genuine and seemly. But in other respects their respective fates would have played into white audiences' expectations -- that black people are good enough to work alongside but not so good to marry, perhaps, or that black people are unhappily different from white people, for instance, inadvertently reinforcing the prejudice that caused that same unhappiness. Shakespeare's treatment of Othello and Desdemona's marriage was bold in some respects, but it's not exactly a well-balanced portrayal -- there are no other leading black characters in Shakespeare's repertoire to counterbalance Othello's grand-scale tragic flaws, or even within the play, and the choice to invoke a white woman's lovely fragility to offset a black man's murderous violence was culturally loaded even in Shakespeare's time. The play seems to have captured a moment in the Early Modern zeitgeist, a historical moment when black people were entering into the familiar sphere of work and marriage but still carried with them the baggage of the exotic and the foreign. Later performances of Othello have been subjected to the racial attitudes of their time and given their audiences scandal for various reasons; within Shakespeare's own time the play itself was titillatingly tragic but not broadly scandalous. Blackness in its international context was somewhat in vogue.

It's not quite accurate to say that the crowd would have been scandalized by the action of the play, or that they would have protested it as reactionary audiences of more recent times might. Blackface performance was a well-worn theatrical trope of the era, and including it in this particular play was not that cutting-edge. The story likely wouldn't have been widely known to uneducated audiences, but it was a reworking of an earlier Italian story by Cinthio called "A Moorish Captain."

That it was not particularly scandalous is supported by the realities of theatre producing at the time. It was an era of very significant censorship, and all plays to be performed had to be approved by the Master of the Revels. In fact, we know from the account books of the Master of the Revels when and where Othello was first performed, and by whom. It was performed in 1604 by Shakespeare's company, The King's Men, at Whitehall, a major royal residence.

This means that the play had royal approval at three different levels; it was performed in King James I/VI's residence (probably also in his presence), by a company that he personally sponsored (all theatre companies had to have some kind of royal patron, and Shakespeare's company was at the top of the list), and approved by a royal official specifically tasked with censorship of inappropriate material.

All of this is not to say that Othello as a character was immune to racist attitudes. His first major speech to the Senate is an explicit defense of (and sometimes apology for) his marriage to a white woman. When the secret marriage becomes known, he is suspected of all manner of witchcraft by reason of his race.

If anything, it's closer to the mark to say that Othello marks a cultural fascination with the (seemingly) irretrievably alien Moors, as Othello premiered just a few years after a group of Moroccan (Moorish) dignitaries came to England on a highly public six month visit. What Shakespeare highlights about Othello is his sense of honor, dignity and power. If he were a little less rigid in his values, Iago couldn't have gotten one over on him.

This kind of fascination/fetishization would go on to become a major trope in English/European literature. By the Restoration (1660-1710) period, the "noble savage" was a fairly common character on stage. Oroonoko (novella by Aphra Behn, play by Thomas Southerne) is the most famous example of this, but the trope was common at least into the mid-Nineteenth Century (and arguably still hasn't gone away).