In high school, I really got into Othello and The Merchant of Venice after being shown the 1995 (with Laurence Fishburne) and 2004 (with Al Pacino) films. In the modern reproduction of these plays both Othello and Shylock are given very sympathetic representations, and the discrimination against them is center place in the plot. I always loved both plays for this, especially considering they where written in the 16th century. I heard though that The Merchant of Venice was actually written as a comedy and that the original theatergoers would have celebrated Shylock's fall. Yet Shylock's speech in the play seems to be highly sympathetic. With Othello, it's even harder for me to read the play as anything less than sympathetic to Othello. I guess I don't have a super-specific question, but how much of my perception of Shakespeare's "progressivism" in relation to race and ethnicity related to my modern reading of his plays? What would be the perception of the plays at the time?
One way to read Othello is that Venice, one of Europe's first true multicultural polities, is caught between two possible competing visions. The first is represented by Michael Cassio, a sophisticated and gentlemanly Florentine scholar-soldier. He represents everything European, Western, and cultured, and is steeped in Renaissance learning. The other vision is represented by Othello, who is a Moor, an "other," strange, and associated with mysticism and magic. He is, in fact, not associated with the Renaissance learning like Cassio is, and instead is ruled and governed by emotion, leading to his easy manipulation by Iago.
At the end of the play, Iago is not killed on stage. Why? This is relatively unusual for a Shakespearean villain, most of whom are killed on stage, or at the very least dead by the play's end. One possible explanation is that Venice is actually indebted to him. By Othello's death, Venice is forced to choose a future represented by Cassio, dragging Venice away from its potential otherness, and into the light of the Renaissance. You are correct that the play is relatively sympathetic to Othello, but sympathy doesn't necessarily mean that Shakespeare believed Othello was the best choice.
So what's behind all of this? At the time that Shakespeare wrote Othello (1603), England is starting to make a broader foray onto the world stage. It has recently defeated the Spanish armada (1588), and Francis Drake has circumnavigated the globe (1577-1580). Depending on what you consider a "colony," England has started its overseas colonial expansion, first with Ireland in the 1550s, and then with the East Indies and North and South America. In 1603 itself, Elizabeth I dies, and James I and VI of Scotland succeeds to the throne, uniting the crowns. The point is, that England is becoming much more multicultural, just like Venice. There may be a lesson in Othello for English society. It doesn't mean that the play is explicitly "racist," but certainly it appears that the play is grappling with ideas of race and multiculturalism and what that might mean for the future of England.
To be clear, this is not the only way to read this play. (For example, another way to read Iago's being alive at the end is that the whole of Venice is ruled by chaos throughout the play, and his continued existence is further evidence of that, as chaos means that justice is not certain to be done.) However, it is one way to read it, and I think even if it's not the primary theme, it is a legitimate secondary theme contained in the work.