That's really a choice each PC makes. My rabbit is one heck of a carnivore (like I am) and loves bacon etc. That said he also has a carrot carrot that I try to make sure to rep with a few crunchy treats a game. It's important to remember that Wylderkin are not the animals they represent, but a unique humanoid races that shares some/many traits with the animal they relate to. Diet is one good option of showing that link, but by no means a required choice.
Food is delicious.
Make sure you wash it first.
If I can get my lobster Kyn off the ground, I plan on eating the smelliest of fish and cheeses to get the point of being a bottom feeder. It's a good thing I like herring and stinky cheese.
XD It's good that those are foods that can be easily cooked out doors.