What is your main goal? Only weight loss, or do you want to improve your diet to reduce inflamation, digestion etc..... Is there is a specific dietary plan/goal you are trying to achieve?
Reason being, is just cutting out those foods may not result in any great loss, if you are just substituting. For example, if you cut out wheat/gluten and replace it with other starches (Rice, potato, beans etc..)... your carb intake will remain same. Doesn't make sense for most people to go gluten free unless they have a gluten alergy or celiac disease. If you cut out dairy, you need to make up the fat somewhere else. Also eggs are one of the most nutritionally balanced foods and has essential fatty acids, same with grass fed butter. Sugar i agree is evil and should be avoided except in very small quantities, but if you cutting out cola and replacing with juices, its still sugar and your body will process it the same.
If you are trying to adapt to a Low Carb, the key isn't just cutting out these foods (and substituting them for healthier alternatives), you need to significantly reduce your carb intake to see notable results, even if its a healthier carb. If you are going for a Ketogenic diet, dairy and eggs are typically a staple on keto (Unless you go Vegan Keto where you need tons of Avacado and Cocount Oil to get your fats), but you must avoid ALL carbs (wheat, rice, beans, sugars, breads, starches). Keto is very strict but very effective.
Anyways, not telling you how to design your diet, but just cutting out those food groups, without a clear nutritional plan and goal, seems a bit unfocused and you may not achieve any big weight loss.
