You have only to look at the kind of taunts that Iago makes to Brabantio to see how race and blackness was viewed. Consider how the darkness of Othello's skin is taken as a symbol of fear, terror and evil in the following quote that Iago shouts out to Brabantio to stir things up:
Even now, now, very now, and old black ram
Is tupping your white ewe! Arise, arise,
Awake the snorting citizens with the bell
Or else the devil will make a grandsire of you...
The use of colour here is hardly accidental. Othello is described as an "old black ram," a metaphor clearly equating being black with sexual lascivity. In addition, Iago says that if Brabantio does not hurry, he will be made a grandfather by "the devil." At the time, white dominated society meant that any visible difference was thought of as being a sign of evil or of something being profoundly wrong with that person, and so it is no wonder that Iago's insults here pick up on common thoughts and ideas about race and blackness of the time.