Dairy sensitivity LO

For those of you who have LOs with a dairy sensitivity did your pediatrician tell you to cut ALL dairy even if it’s in the ingredients of something? My LOs ped told me it doesn’t matter if it’s in the ingredients as long as it’s not straight cheese, milk, butter. So if I buy waffles or poptarts with dairy in the ingredients it will be fine but if I have Alfredo it’s not ok.