I believe a person cannot attain spirituality while their body is constantly full of toxins including red meats and processed foods. In order to attain spirituality, the body must cleanse itself and remain free of these harmful contaminants. The Jainism vegetarian diet provides nutrients the body needs without including meats or processed foods. This allows the body and it's systems to be healthier and more able to attain true spirituality.
Vegetarian and vegan diets help in someone's spirituality in that the alleged spirits of animals aren't sacrificed for the food of humans. Plus, vegetarian diets aid in keeping the mind focused and are better for you nutritionally. Even thousands of years ago, practitioners of Jainism knew what to do when it comes to having a karmically-correct diet.
Unless a person needs to eat meat for health reasons, a vegetarian or mostly vegetarian diet can assist one in developing a deeper spirituality. One feels lighter as a physical being and one is clear about not taking in the flesh of another living being, especially if it has been violently killed.
To them, this diet is very helpful to aid in their belief. It is all simply what they keep faith in, and what they believe helps them through life. They like to believe in a higher power that helps them through life, and they believe a vegetarian diet helps achieve this.
No, Jainism vegetarian diets do not help in spirituality. Personally, I do not really think anything can help you become more spiritual as I do not subscribe to supernatural things. Although I am a vegetarian, I don't get any sort of spiritual benifit from it. I am a vegetarian because I do not agree with the beef industry.