Steven can describe your cat as "queen of the short bus" after inflicting your cat with a fictionalized memory disability as punishment for save scumming.
the disorder "Scatological" apears in game and makes your cat have an unresistable urge to eat poop the disorder "Pica" also apears and makes you cat eat coins instead of simply picking them up
the player can unlock a "gaydar" abilty to tell if their cats are gay bi or strait. but since they are cats i don't think they have a consept of a closset
okay so..... hitler himself shows up as a boss... however he is super heavly mocked as he repeatly executes his own loyal minions (who are also his clones) for "daring" to get hit in a turn based game. and also kills himself when he gets to low health.
while Anxiety is present in the game it does not give a cat a random chance to get feared. However cats can also get "The Shining" that does have a chance to fear them at the start of the turn
Characters in the game treat cats as disposable resources, make them fight, use them for science experiments, etc. The tone is satirical and most of the violence tends to be the cats actually fighting each other.
Dogs don't feature prominently, but in their place there's plenty of cat fighting to serve the same purpose. There is a character that trains cats to fight and asks you to send him cats with "combat experience" who can "take a punch."
an alien enemy type called "B-Prober" has a very phalic looking probe that they use as a weapon and can insert it into a cats butt to temporarly control them.
Maybe not in a way that will be actually effectively horrifying, given the artstyle, but the game is about breeding cats to the point that they mutate, and encountering mutated/disfigured creatures in the wild.
There are cultists who cut themselves, and it is crudely animated. There are abilties that allow you to hurt yourself to gain a gameplay benefit, one is called "self harm." There is a sort of emo eyeshadow mutation your cats can receive that gives you a damage bonus if you're bleeding. Not sure if this will be triggering to anyone because of how cartoonish and detached the portrayals are.
the disorders, Crohn's Disease, Dysentery, Incontinence, Irritable Bowel Syndrome, and Kidney Stones (debatebly), can make a cat wet/soil themselves. how ever its not like they are wearing pants in the first place so does it even realy count?
Autism is framed as "-2 Charisma, +2 Intelligence. The spells you were born with cost 2 less mana. Your other spells cost 1 more mana." This is an oversimplification but the game is not trying to depict each disorder/condition in it accurately, isn't trying to be harmful, and is not meant to be taken entirely seriously.
Various vulgar language as well as references to crass subject material, on-screen and off. Steven mentions the game he's originally from which itself has a vulgar title.