Your reputation with the four nations changes with capturing or sinking.
Pirate:
Capturing or sinking a pirate convoy increases your relationship with all nations. This also applies to pirate hideouts.
Buccaneer:
A fight against a buccaneer with a Letter of Marque for the respective nation results in a relationship loss with all nations. With a Letter of Marque you only lose your reputation with the buccaneers nation.
Bounty hunter:
It seems that fights against bounty hunters do neither harm nor improve your reputation.
Unpopular competitor:
From time to time you receive the mission to harm a competitor. If you accept the mission you will lose reputation with all four nations - it is an act of piracy.
Drunkards:
The drunkards mission is not related to a reputation change, like the fight against bounty hunters.
