I like dairy. My people like dairy, and aged cheeses (actually even fresh cheeses) give me no problems. So I pick dairy as the one to include for a vegetarian. But if cheese (and yogurt) give you problems, you should stay away from them. If I understand ghee correctly, the milk solids are cooked out or separated from the final product.
I know in my brain that grain is stupid for me to eat, but it has never given me any major problems (I don't consider a little bit of flatulence to be a major problem). I allow myself a serving of wheat per week. I don't always eat it, but I allow it. But if tomorrow, my doctor said, "Girl, you have to stop eating wheat or die," I'd toss it like yesterday's garbage. I also don't think most grains have much nutritive value, where some dairy products really do.
"Right is right, even if no one is doing it; wrong is wrong, even if everyone is doing it." - St. Augustine