No. I am a vegetarian, but haven't put my cats and dogs on vegetarian diet, and do not want to experiment with that.
I love animals, and bet you do to if you are interested in plant-based diets for pets. However, if we undertake caring for another living thing then it becomes our responsibility to provide fully for their needs. While I can be fine without meat, cats and dogs have different dietary needs than we do as humans.
Cats are obligate carnivores, meaning meat is an essential part of their diet, they can't eat a substitute. The ingredient of taurine which comes from animal tissue is ubiquitous in reputable cat food. Without taurine the health of a cat will deteriorate eventually, it hinders their growth development, leads to blindness, heart failure. If a cat doesn't get ths key vitamins that only come from meat then sadly it dies.
https://vcahospitals.com/know-your-pet/taurine-in-cats
https://pets.webmd.com/features/vegetarian-diet-dogs-cats
Dogs are also carnivores. Unlike cats dogs are scavengers that can make due when no meat is around, but just being able to survive in a taxing situation is not the same as thriving as Dr. Karen Baker points out below. I want any dogs I raise to reach their full potential, not live but with possible protein deficiencies, dental problems or anything that makes their life more of a challenge than it needs to be.
https://www.google.com/amp/s/health...04/amp/dog-cat-species-appropriate-diets.aspx
https://www.dogfoodadvisor.com/canine-nutrition/dogs-carnivores-omnivores/
If you are looking for a pet companion, but not comfortable with purchasing petfoods that include meat, then have you thought about a pet rabbit, turtle, goldfish, parrot, horse, iguana, guinea pig, rat? There are a lot of omnivores and herbivores that make good pets too.
If you have cats or dogs or are sure that you want to adopt one then be brave! They want meat, don't change their diet. Feed them what nature prefers they eat. There are some conscientiously-sourced pet food that use free-range and vegetarian-fed chicken, don't do animal testing, donate percentages of their proceeds to local animal shelters, and have many other positives that help animals and the environment. I opt instead to patronize those brands, rather than buying vegetarian cat or dog food. I see this as a middle path that enables me to give my pets all of the vitamins they potentially need, while still lessening the suffering of other animals in the world.
I hope that helps. If you ever want to talk with me about animals shoot me a pm