No, but pets, including dogs, can be fired out of cannons. This will frighten them, and they will be covered with soot, but they will not die or be visibly injured.
In-universe no one is misgendered but a large part of the playerbase misgenders the Servant of the Flame. Most do it unintentionally because their pronouns have only been confirmed outside of the game so far by the developers.
Bounty skulls whisper to you wordlessly--it doesn't trigger mine but I'm sure it could for some people. Squeaking from rats and ships, probably other stuff I can't think of.
Bigoted players can and will target players flying the rainbow flag on their ships (speaking from personal experience). No confirmed LGBT NPCs have died.
Merrick used to be an alcoholic, but seems to be in recovery now. Players can drink excessively, and it is possible to fire cursed cannonballs to intoxicate everyone on a targeted ship.
It is possible to hunt and kill animals, but there is no obligation to do so. Characters in the Hunter's Call will talk about some of the animals they have killed.
Can naturally spawn on some islands and attack the player by spitting venom, there is an island called Snake Island where they spawn the most from my experience
Characters will have randomly generated scars, some of which could be interpreted as self harm. Players can be injured by swords, although they leave no physical wounds.
You can choose to temporarily lock your own crew members in the brig, but this is usually justified because of bad behaviour, and you can't do it to your enemies.
Undead skeletons carrying gunpowder barrels can run up behind you and explode. Lightning strikes can hit you or your surroundings unexpectedly. Enemy players may ambush you with cannons or gunfire.
Drinking excessively or eating raw food or fishing bait will cause the player to vomit. If someone is vomited on, their screen will temporarily be covered in green slime.
Underwater shipwrecks are disorienting, making it easy to get trapped. The Kraken can grab you and dunk you underwater. If you upset your crew members, they can temporarily lock you in a small cell. Most caves are relatively spacious, but can be dark and you can get lost.
Players and NPCs can use several guns, such as one-shot rifles, shotguns, pistols, and cannons (all of this along with swords and daggers), as this is a pirate game.