Not only is Starbuck's anger with Ahab reasonable, Starbuck functions as the main voice of common sense and rationality in the novel. Moby Dick is such a grotesque and multi-faceted literary work, so full of symbolism and meditations on the human condition, that it is easy to forget the simple practicalities of the narrative. Whaling ships did not go to sea in order to pursue personal vendettas against specific whales. They were money-making concerns, aboard which crews endured hardship and long separation from their families in order to procure as much whale oil as possible. For the owners of the ships, they were speculative ventures in which a large investment of time and money might yield large returns.
All this is so obvious that it is surprising to find anyone following Ahab's mad scheme for revenge rather than Starbuck's idea that the Pequod should pursue the same rational mission as every other whaler on the ocean. Unfortunately for Starbuck, he lacks Ahab's charisma and power.
What you would do will depend on your personality and your values and how prepared you are to take risks. Starbuck considers shooting the captain, but he does not do so. Is this weakness or honor? You might approach this by thinking about what action would have been most likely to succeed. It is obviously a lost cause to try to change Ahab's mind. If Starbuck had shot him, would the men have followed Starbuck? Would his death have broken the hold he had over the men, or would they be loyal to his memory? Would an attempt at revolution involving the other mates have enjoyed more success? All these courses of action are dangerous, but it is arguable that failing to challenge Ahab's leadership is the riskiest course of all.