Othello - racial slurs and stereotypes

Act one, scene one of Othello surprised me with some immediate racial slurs and stereotypes. I might not have picked up on as many of these that I did if I hadn't been reading from the Sparknotes website I mentioned in the previous post (while I did try reading the original version, I kept finding myself getting distracted by the translation which read through much faster).
Iago shows some true disrespect for the Othello when he goes to Brabantio to report that he was sleeping with (and secretly married to) his daughter, Desdemona. He refers to Othello, the Moor, as a "Barbary (African) horse" and goes on to say that he will have black, neighing grandchildren if he doesn't get a handle on his daughter. Earlier in the scene, he calls him "Thick Lips," which is clearly a racial slur.
The point I'm trying to make about all of this is that I'm surprised by how this kind of talk was apparently acceptable during Shakespeare's time. I'm sure it was the politically-correct, suburban atmosphere that I grew up in that taught me that it is not acceptable to refer to people in such a way. I guess it is naive of me to think that everyone has always been this way.
I also still can't help but be surprised that, even hundreds of years later, we are still dealing with biracial relationship issues. Wouldn't you think that we would have gotten over this obstacle by now? Seeing Shakespeare write about the types of social problems that we still deal with today really makes me wonder how we can be so slow in accepting the differences amongst the human race. We have made a lot of progress, but seeing the same problems displayed in Shakespearian times really demonstrates the slow rate at which the society of a human race can move when developing acceptance.
In the second scene of Act Two, there is a part that made me directly think of Hollywood nowadays. From lines 64 to 83, Barbantio is on a rant about how Othello needs to be arrested for black magic. How else could a Moor sway his innocent, law-abiding Italian daughter to marry him? This part is definitely straight out of a Hollywood film, where the daughter is told that she simply can't be with the man she loves becauase he is of a different race. In the movie Cruel Intentions, Cecile (a white girl) is told that she can't be with her cello instructor, Ronald simply because he is black. I can't even begin to name off all the movies or television shows out of Hollywood that tackle the race subject. Barbantino is so unwilling to accept the love between his daughter and Othello that he assumes there must be some sort of evil magic being used. Similarly, in Cruel Intentions, Cecile's mother accuses Ronald of acting on a bet instead of simply wanting to be with her daughter.