Simply put...if I should stop consuming the nutrient dense foods during the protocol I'm not sure what is safe to eat? By the quote you provided it suggests to me that the MMS is doing it's job without the aid of nutrition but for me it would be reckless to consume foods that lack any nutrition as that is simply poison.
Healthy eating is never a mistake.
"Healthy eating" might be defined as simply eliminating toxic substances from the diet. When attempting to restore health and following MMS protocols, what you SHOULD NOT eat is more important than what you DO eat.
We know that Vitamin C supplements, orange juice, coffee, tea, alcoholic beverages neutralize MMS - therefore start out by eliminating these things from consumption. Though as a caveat, if I was treating myself for cancer, I would take 1 gram of Vitamin C in the evening 2 hours after my last dose of MMS. The immune system is greatly impaired without Vitamin C. If one can afford the cost, Vitamin C in the form of Camu Camu or acerola cherry should be considered, since they are food in comparison to ascorbic acid - which is a chemical produced in a lab.
Next, sugar and grain should be eliminated from the diet. Sugar poisons the body in a hundred different ways, is a hormone disruptor, disables the immune system, and feeds troublesome microbes such as Candida yeast. Wheat gluten causes autoimmune diseases such as rheumatoid arthritis, digestive disorders, skin diseases, elevated insulin levels, and nowadays wheat is sprayed with Roundup (glysophate) at harvest time. Soybean products are hormone disruptors, interfere with the uptake of iodine and other important minerals, and therefore should be eliminated from the diet.
Processed seed oils such as soybean oil, Canola oil, corn oil, sunflower oil, safflower oil, cotton seed oil, are highly toxic. Anything containing these oils as an ingredient such as margarine, mayonnaise, salad dressing, baked goods such as crackers should be eliminated from the diet. Likewise, anything cooked in these oils such as fried chicken, fried fish, french fried potatoes, etc. These toxic oils should be replaced in the diet with healthy oils such as hemp seed oil, flax seed oil, unrefined sesame oil for salad dressings and virgin coconut oil and unrefined sesame oil for cooking. Replace margarine with butter. Pasteurized, homogenized milk should be replaced with raw milk.
Thyroid problems most often result from exposure to bromide, fluoride, and soybean products - and lack of the minerals iodine and selenium in the diet. Bromide is used as a dough conditioner in commercial baked goods. Fluoride is in un-filtered, un-distilled water. I suggest buying a reverse-osmosis water filter, a water distiller, or a counter-top water filter that uses tricalcium phosphate (bone char) as a filtering media. Fluoride is a powerful carcinogen, so one should make their own toothpaste and avoid drinking anything that comes in a bottle or a can. When attempting to restore health, I suggest drinking nothing but purified water - at least 2 liters per day. Kelp tablets are a food source which provides iodine, but should not be taken until the end of the day 2 hours after the last dose of MMS. Like Vitamin C, iodine is a powerful anti-pathagen - so one need not worry about troublesome microbes feeding on it. Brazil nuts (which come from Brazil) are the richest food source for selenium.
Since you mentioned you're following Protocol 2000 and the Gerson Institute, I'm assuming you are recovering from some form of malignancy. We know that while normal cells can burn either glucose or fatty acids for energy, cancer cells can burn only glucose. The liver produces glucose from carbohydrates, including sugars, grains, starches. By eliminating carbohydrates from the diet, the cancer cells literally starve to death. This is called a "Ketogenic Diet," which involves minimizing carbohydrates and using fats as the sole source of energy. Not necessarily animal fats. Avocados, olives, and seeds such as raw sesame seeds, chia seeds, raw sunflower seeds, raw pumpkin seeds, along with nuts such as walnuts and pecans are very high in healthy fats and calories.
Cod liver oil is a food which provides Omega 3 fatty acids, Vitamin A and Vitamin D - all of which are important in preventing and recovering from cancer. The best source of Vitamin D is direct exposure to the mid-day sun with as much bare skin as possible. Apparently wearing sunglasses interferes with the production of Vitamin D in the skin.
In summary, I suggest eliminating the known toxins from the diet - and then eating all the raw fruits and vegetables that you want. Cut back or eliminate carbohydrates as best you can, and derive most or all of your calories and energy from healthy fats. As CLO2 and Rev Paul advised, eat small meals before and after your MMS doses, since MMS seems to work best on an empty stomach.
Archbishop Jim Humble has written that "nutrition from supplements" feed pathogenic microbes, and I won't contradict that. However through my research I've formed the opinion that pathogens primarily feed on sugars, excess carbohydrates, toxins and poisons (which is why God created them). I'll restate my belief that healthy eating is never a mistake, and that healthy eating will compliment rather than interfere with the functioning of MMS. What would be the alternative - eating junk food to improve the efficacy of MMS? In the U.S., to eat "normally" is to eat junk food.