Zootopia didn't touch on this topic, but Beastars solved the problem by making all foods vegetarian (substituting meat with high-protein vegetarian alternatives resembling meat, including soy, or seafood options, since I don't think any of the characters were sea animals or bugs)---and even then there were societal divides caused by what they called devourings, as well as a black market that distributed either ethically or non-ethically sourced meat products. The ethically sourced meat came from hospitals (animals who were already dead). Non-ethically sourced meat came from... well... anywhere from covertly breeding livestock to herbivores selling their own limbs. Even among carnivores the black market remains an ethical dilemma.how would carnivores even survive in such a society?
So, surely, there would be supplements and alternatives to meat, but there is definitely no clear-cut answer and carnivorous animals are still carnivorous animals. I suppose some of it depends on which animals are anthropomorphic and which aren't, and what means are available to substitute or fulfill those needs