What is the "reaction" I'm trying to avoid when instructed to use a nonreactive bowl?
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The reaction you're trying to avoid is some chemical process where the vinegar/acid in the recipe reacts with the metal in a reactive bowl resulting in a 'metallic' taste. Depending on the ingredient, sometimes the colour is affected
the reaction you are trying to avoid is loosing the air/fluff/peaks when beating something in a nonreactive bowl?
Food acids (in vinegar, fruit juices, wine, etc.) combine chemically with metals (especially iron and copper) to form undesired compounds. If you've ever slow-cooked tomato sauce in a cast iron pot, you've seen the very dark-colored results.
Aluminum, on the other hand, reacts with bases (such as baking powder and baking soda), so batters should not be made in aluminum bowls. However, baking pans are usually not subject to this result, either because they've been coated with a non-reactive coating or because moist alkaline compounds are not in contact with the aluminum for very long (the part in contact with the metal cooks first, quickly converting the alkali to carbon dioxide for leavening, and forming a barrier that keeps unconverted basic compounds away from the aluminum). Very light-colored sauces should not be made in pots in which aluminum is exposed, either -- stirring can dissolve their protective layer of aluminum oxide, turning the sauce an unappetizing shade of gray.
"Non-reactive" usually refers to plastic, stainless steel, ceramic or glass. Obviously, ceramics that have been glazed with lead-based glazes (common in many imported clay dishes and pots) should be avoided, as food acids can leach lead from them.