What can we make of Iago’s “seduction” of Othello in act 3, scene 3? Should Othello be more suspicious of what Iago, or are we sympathetic to Othello falling into his trap? Ultimately, can we justify Othello siding more with Iago than his own wife?

In act 3, scene 3 of Othello, Shakespeare shows us a side of Othello that we haven't seen before. Othello has expressed some concerns and self-doubt regarding his color and his age previously in the play, but he has otherwise appeared supremely self-confident, even-tempered, and rigorously fair-minded.
Othello forestalls a brawl in the streets with Desdemona's father, Brabantio, and others by the force of his personality alone. He likewise disarms the Duke and his council, figuratively speaking, defends himself for eloping with Desdemona, and wins them over with his description of how he won Desdemona's love. The Duke even rewards him with command of an expedition to Cyprus.
In act 2, scene 2, Othello acts every inch the soldier, general, and commander, dispatching letters to the ship's captain, and taking charge of the fortifications of the castle.
In act 3, scene 3, Othello is suddenly cast as a secondary character to Iago. Othello seems to be much too easily led by Iago's insinuations, asides, and remarks made under his breath about what Iago wants Othello to believe is an affair between Desdemona and Cassio.
Othello and Iago watch Cassio and Desdemona from a distance (an unusual perspective for Othello) for only a moment, but it's time enough for Iago to cast aspersions on both Cassio and Desdemona's characters. Iago plants a small seed of jealousy in Othello's mind, but the jealousy grows far out of proportion to what the audience knows is an innocent meeting between Cassio and Desdemona. Desdemona doesn't help Othello's perception of the situation by so forcefully advocating for Cassio with Othello to return Cassio to his position and duties as Othello's lieutenant.
By the end of the scene, Iago has so manipulated Othello that Othello is beside himself with jealousy. This is the same Othello who just one scene before was commanding an army. One scene later, he doesn't realize that he's being manipulated by Iago, and he can no longer control his emotions.
Othello impotently strikes out at Iago, the messenger of the news of Cassio and Desdemona's supposed affair.

OTHELLO: (to Iago) Avaunt! be gone! Thou hast set me on the rack:I swear 'tis better to be much abusedThan but to know't a little. (3.3.374-376)

Othello has totally lost control of himself. He's lost all perspective, and he's wallowing in despair and self-doubt.

OTHELLO. Villain, be sure thou prove my love a whore;Be sure of it. Give me the ocular proof;Or, by the worth of man's eternal soul,Thou hadst been better have been born a dogThan answer my waked wrath! (3.3.399-403)

Othello desperately cries out for proof of the affair.

OTHELLO. Make me to see't; or at the least so prove it,That the probation bear no hinge nor loopTo hang a doubt on; or woe upon thy life! (3.3.405-407)

Iago gives Othello only insinuations, which by this time is sufficient to drive Othello mad, well beyond reason.
It seems out of character that Othello doesn't confront Cassio directly about the supposed affair. Othello had no difficulty whatsoever confronting Cassio about his drunken brawl with Montano in act 2, scene 3, and relieving Cassio of his duties as lieutenant. Iago completely disarms Othello to such an extent that Othello has no defenses, and he feels unable to respond in any rational way to the situation he's facing.
As to whether we should sympathize with Othello or hold him responsible for his own behavior, we need to remember that Othello is the victim of a ruthless, hateful, master manipulator. For all of his good qualities and his real-world skills as a soldier and general, Othello is no match for Iago's skills as a villain.
To our mind, yes, Othello should have advocated for his own wife, but Iago managed to cause Othello to distrust and disavow his own logic and reason, and he induced Othello to question and then abandon his heretofore all-consuming love for Desdemona.
Iago discovered a flaw in Othello's character that only Iago could see. It was a flaw that perhaps only Iago could manipulate to drive Othello to such a rage of jealousy that it ultimately resulted in Othello and Desdemona's downfall and destruction.

Othello definitely should have sided with his wife. However, Desdemona and Cassio make themselves look guilty when Desdemona is telling Cassio that she will help him get his job back, and Cassio kind of slinks away as soon as Iago and Othello show up. Othello asks Iago if it was Cassio he saw leaving, and Iago lies. He tells Othello that Cassio would have no reason to look so guilty.
Iago starts to "seduce" Othello by reminding him that Cassio was the go-between when Othello and Desdemona began their courtship. This is a really sneaky, underhanded thing to do.
Iago starts to hint at the possibility that Cassio is less than honest, until Othello yells at him to speak his mind. Iago then finally tells Othello that he should watch Cassio and Desdemona, to make sure that they are not having an affair.
Again, Othello should have trusted his wife when she assured him of her faithfulness. But he starts to doubt himself when he is alone. He starts to think Desdemona might no longer love him, because he is too old for her or because he is black. Iago plants the seed of mistrust, and Othello acts upon it, so they are equally to blame for the tragic events that happen at the end of the play.