The protagonist is shown to have been knocked out and tied up by a Mexican gang. However, they merely intended to assign some tasks to him and immediately let him go, so it's not necessarily kidnapping.
A scripted scene involves the protagonist getting knocked out by a guitar. Certain non-lethal weapons are also designed to knockout NPCs without killing them. (most likely intended for a pacifist run of the game)
If the player chooses to use the crack pipes for filling up their HP, the protagonist will lose a chunk of the HP from withdraw if crack isn't smoked consistently afterwards.
Rabbits and pigeons roaming around the open world can be killed. Some optional challenges require the player to kill a certain amount of rabbits. A sewer mission also involves the player having to fend off hostile rodents.
One mission involves bringing 3 cats and 3 dogs to a shady character that never shows his face. Given POSTAL's history of blatantly implying certain NPCs to be serial zoophiles, it can be interpreted as the same thing here. There are also scenes involving animals in a sexual context, (mainly the protagonist having intercourse with a cat while lucid dreaming as one and a male rabbit pleasuring itself with a sex toy) however no animal is ever forced into a sexual encounter.