Health is, without hope of argument, wholistic. It involves all tangible and intangible parts of the human being. Lean meats and dairy products are optional. You can still choose to consume animal products as part of a plant-based diet, so long as plants comprise the foundation of your meals.
Vegetarianism is encouraged, but by no means dogmatically essential.
Buying organic is expensive, but advantageous. However, I will say that the Standard Western Diet is generally too high in fat and protein. God designed our bodies to run on primarily clean-burning complex carbohydrates. High fat, high protein eating styles displace needed carbohydrates, plus the excess fat and protein is in itself destructive. Please, please research the matter carefully before subjecting your body to a low-carb diet.