You only see it if you backtrack after a certain point in the game, but a dog and a cat are shown to be waiting for their owner--who is heavily implied to have been killed in a recent military conflict--to return.
Though this should not be interpreted as deliberately abandoned. The parent is whisked away to a far away place by a powerful force and can't find a way to return to his child.
One of the summons resembles a unicorn; it can be killed when it's on your side, and there are multiple occasions when it's not on your side and you have to fight and kill it yourself.
At the end of the game, you are forced to kill numerous non-human characters (several of which do resemble animals) that one of your party members is emotionally attached to. She is in visible emotional pain after each one is
killed; for some it may invoke the feeling of having to put down a pet.
No hanging but a trial ends with the sentence declared being execution. Shown as being sent to labyrinth with monsters and a water tunnel with monsters
The player has the option to have the POV character flirt with women who aren't his main love interest, (and they may flirt back if their affection values are high enough) but this doesn't prevent them from getting together.
While relatively mild when compared to real-life hate speech, there is a race of people that is heavily discriminated against by many members of the other races.
One of the protagonists is 17 (Yuna) and she marries someone who is 28 (Seymour). She doesn't love him. They are shown kissing and he flirts with her all the time.
A male character's father constantly berates his for crying or for potentially crying in response to a variety of situations. The story treats this as abusive behavior.
A sea creature bites a fish with a spray of blood, and a summoned creature bleeds from the eye in one cutscene. These are the only cases of blood shown in the entire game.