Racist attitudes were indeed endemic to Elizabethan society as the world was still a small place with little appreciation for difference. Othello as a Moor was unique in the circles in which he moved, and this made him a fascinating character. Indeed, this is how he came to be welcomed into Brabantio's household and how he and Desdemona became close.
Othello clearly understands how his relationship with Desdemona will be viewed: that he wil be seen to have bewitched her. He says to the Duke in Act I scene iii
I will a round unvarnish'd tale deliver
Of my whole course of love; what drugs, what charms,
What conjuration and what mighty magic,
For such proceeding I am charged withal,
I won his daughter.
Brabantio is devastated when it is revealed that Desdemona is a willing part in the elopement, and dies of grief as a result. He cannot reconcile himself to the betrayal he has suffered.
Iago is more concerned with his general misanthropy: he dislikes every human being, not just Othello. He has an equal measure for dislike for Cassio and even Desdemona. His motivations are beyond racism.