What if you grated apple and put it on bread? It's white too. Apple sandwiches were one of our favorites as kids.

Jacket Potato with optional extras do they can make their own (my kids love being involved). We put these in small bowls on the table and kids can choose: sour cream, avocado, tuna, cheese, corn (that way dd gets lots of choices and other two are limited only by their specific requirements each).

Wow it's a tough combination of issues. I can think of lots of white but then it has dairy or egg, then lots of egg and dairy free but not white!