There are two main story missions that involve hunting that can't be avoided. The first one involves hunting two deer in the first chapter of the game. The second one involves hunting a bear early in the second chapter.
There are also some parts of the story where you have to shoot wild animals like wolves, especially in the first chapter. And you will run across aggressive animals while roaming free as well, and they'll kill you if you don't shoot them first.
The crafting aspects also involve animal products, but you can probably ignore them. The advantages are relatively minor, it's mostly just increased inventory size. You can also buy the improved satchels after the end of the main story without hunting.
You need to eat somewhat regularly in the game, but you can buy food in stores. It's much cheaper to hunt and cook, but it's easily possible to survive without hunting. I don't think anything happens if you don't provide provisions to the camp, but I never tested that fully.
But in general, if you strongly dislike hunting it's the wrong game for you. I would also warn you that many aspects of hunting are very realistic. If you don't hit the deer fatally, they will make heartbreaking sounds until you kill them. If you strongly dislike even virtual animals suffering, don't play the game.