Is Othello too gullible to be a sympathetic tragic protagonist?
I would assert Othello is not too gullible to be a sympathetic tragic protagonist.
Admittedly, the way the play is structured, Othello can look gullible—especially from our twenty-first century perspective. We can be swayed to this interpretation because Shakespeare uses dramatic irony. This occurs when the audience watching or reading a play knows something the characters do not. In this case, we as the audience have access to Iago's thoughts. We know from the start that he is an evil individual who wants to destroy Othello. The reason Iago gives for his hate is Cassio being promoted over him, but his anger is so intense it seems far deeper-rooted. So Othello can look gullible because we know so much more than he does about Iago.
However, Othello himself has no reason to suspect Iago's hate. All Iago shows him is a pleasant, loyal face. In fact, Othello is not alone in being deceived by Iago: everyone around Othello is also taken in. If others could see Iago's nature and Othello couldn't, it would be more plausible to interpret Othello as naive. Part of the tragedy of this play is that Iago is able to deceive all the people who count.
Othello can look extra gullible to us because we live in a society that values the word of a woman as equal to that of a man (at least a little more often than in the Renaissance). In Othello's far more patriarchal world, it was more plausible for a male to believe the word of a male friend against that of woman. Othello is a product of his culture when he believes Iago's lies and insinuations about Desdemona and Cassio—and disbelieves Desdemona's protests of innocence in the moments before he kills her.
Othello also trusts Iago because he himself is a trustworthy man. We tend to evaluate others by what we are, which is why Iago sees everyone around him as filthy and corrupt. (In Desdemona's case, Othello's natural trust is eroded by his insecurity that a beautiful young woman could love him.)
Othello is not so much gullible as tragically taken in by an especially warped person who manages to play on his strengths and weaknesses to destroy him.