During Otto Baynes' campaign when meeting Ezequiel in the café, if you choose not to fight him, he will be ridiculed as a coward upon his return to England to inform the King they chose not to fight, and will be renamed to "Loser Baynes". Upon returning to Spain and accepting Ezequiel's duel, defeating him will cause him to express confusion as to why Otto backed out of fighting him the first time before proclaiming that he will never be called a loser again, changing Otto's name once more to "Winner Baynes".
Contributed by MehDeletingLater
During Catalina's campaign before the final boss fight, there are two different scenarios that occur if you decide to attack either João or one of the ships in Ezequiel's fleet first (implying that she thinks they are still her enemy) that make the game unwinnable.

Upon attacking and defeating Ezequiel's fleet first, the ships following you will stop and instead travel around the overworld in random directions until they eventually disappear from the map. Despite this, João's ship will still follow behind her, and defeating him will cause his ship to disappear entirely.

If you attack and defeat João first, his ship will disappear and cause the rest of Ezequiel's fleet to scatter. In a fourth wall break, Catalina will point out upon attacking João that she chose to do this just to see what would happen, before he encourages her to reset the game so they can see the ending.
Contributed by MehDeletingLater
Towards the end of João Franco's campaign, breaking the flow of the game's story by choosing to attack Catalina's fleet will prompt his crew and opponent to mock him for being spiteful against her, causing him to be renamed to "Spiteful Franco" and significantly reduce his stats, making the game unwinnable. Upon her defeat, Catalina will then appear on the overworld as a hirable vagabond sailor.

A similar situation occurs when attacking Ezequiel's fleet, causing João to be lambasted for making such a poor decision, renaming him to "Nitwit Franco", and dropping his stats to the same unwinnable level.
Contributed by MehDeletingLater