What is a "nonreactive" pan?
Try cooking tomato sauce in a cast-iron pan some time... You'll learn a whole new meaning for "irony". 

A non-reactive pan is one that allows you to cook or store acidic foods without dissolving, leaching, or otherwise causing contamination. Good materials for such pans include glass, stainless steel, food-grade plastic, ceramic, porcelain, and hard anodized aluminum. Bad materials include cast-iron, copper, and aluminum. 

Plastic bowls should be fine for most purposes, however keep in mind that small scratches in the plastic may harbor contaminants that will be freed by the acid. So clean them well, or switch to glass.