This question might seem like an easy one to answer, and a few years ago it was, but now there is debate amongst the food allergy community as to whether potentially cross contaminated foods should be avoided.
Up to 7% of foods tested that had warning labels such as “may contains peanuts” or “manufactured in a facility with peanuts” contained detectable amounts of peanut protein even though peanut was not a listed ingredient. This “could” be enough protein to cause a serious reaction in some allergic individuals. In fact, some severely allergic individuals have had very serious reactions to such foods.
However, some allergists now believe that potential trace exposure of allergens can be more helpful than harmful (in some individuals). The idea being that trace exposure (via ingestion) creates desensitivity much in the same way as many of the current food allergy treatment studies.
Because no allergy or allergic individual is the same and because there is no way to tell how much of an allergen might be in cross contaminated food; we recommend avoiding foods with any type of warning label. Or at the very least consult your own allergist based on your own situation.