"Western" disease is caused by high intake of processed foods, soda, etc. It isn't the vegan diet that helps. It's removing processed food, soda, etc. You can be an omnivore or a carnivore and remove processed junk food and reduce "Western" disease. And you can be a vegan and eat a ton of processed vegan junk food and succumb to "Western" disease.
Processed foods and overeating is the true problem in the western diet.