One problem with asking whether William Shakespeare's Othello has "racist" undertones is that the concept of "racism" as we now frame it is a uniquely modern (20th/21st century one). Through the 19th century, different races were simply assumed to have different types of character and intellect, just as they might have different physical appearance. For example, Aristotle believed that pale northerners were sluggish and stupid compared with darker skinned Greeks.
Shakespeare probably based Othello on works about the Moors suggesting that they were candid but prone to jealousy. In that sense Othello is a racial "type". Critics are divided over whether Iago plays on an existing fault in Othello's character (jealousy, being prone to insane rage) or whether Othello really is noble and innocent. In all cases though, the real villain is the Italian Iago, not the Moor, and thus it would be hard to say that the play is anti-Moor.