Vegetarians don't eat tuna. Some who call themselves vegetarians opt to eat tuna and other fish, but the North American Vegetarian Society considers those people "would-be vegetarians."
The Vegetarian Society says that fish hasn't ever been acceptable for vegetarians because fish are cold-blooded animals who are sometimes subjected to cruelty. The NAVS points out that fish feel pain and fear when hooked or netted, and turtles, dolphins and other animals often die when they become entangled in nets meant for fish.
For some vegetarians, eating a proper amount of protein is the driving force behind the desire to eat tuna. Vegetarians can eat beans, lentils, nuts and tofu to get the protein they need, according to ChooseMyPlate.gov. Some ovo-vegetarians opt to eat eggs as a source of protein.