In Shakespeare's Othello, how does racism affect the relationship that Othello has with Desdemona, Roderigo, and Iago?
If you are going to examine the idea of racism in Othello, you have to at least consider what you mean by the term. Are you looking at it from a 21st century perspective? Well, of course you are. Your own preconceptions and what you see in the text are going to be very different interpretations than what someone a century ago would have perceived. So, you need to consider what the term "racism" might mean as it pertained to Elizabethan England. You can call Shakespeare a racist, or you can consider that perhaps he was looking at the character as more of someone who is an outsider, a foreigner, than just a black man.
Given that, you could say that Desdemona was a reverse racist in some respects, since her attraction to Othello had to do with the fact that he was so different in every way from her.
Roderigo, as well, does not necessarily see Othello from a place of race; his concern is the fact that Desdemona has rejected him and married someone else, someone so different. Remember, Roderigo is Desdemona's social equal, so he cannot fathom why she would choose Othello.
As far as Iago goes, he has a whole slew of reasons to justify why he wants to be the means by which Othello is brought low. Race is only one of them.
Does the fact that Othello is black perhaps affect the way the other characters respond to him? Sure, buy it isn't so straightforward as simply out and out racism. It's a complex play, and he is a complicated character.