Do storms influence the souring of dishes? The story/lore passed from generation to generation is about the influence of a storm on some dishes. Allegedly, they sour once the storm hits. This holds especially when the dish is kept in a metal bowl, jug, or pot. What I've heard is that it affects soups, broths and mayo-based salads the most, but I am not sure if that is because of their ingredients or just because they are mostly kept in those metal containers. 

Is there any scientific proof of this phenomenon, and if so what is the mechanism? Is it due to rapid changes in the air pressure or maybe electrostatics? 

If that would be true, how can one counteract it? Does keeping dishes in the fridge help?
The short answer is no, storms don't cause souring.  Souring occurs because of bacterial or yeast growth.  Sometimes this is desirable, sometimes not, depending on your goals.  If by "souring" you mean spoilage, proper sanitation and refrigeration are your best protections.  Sometimes the composition of a food container can impact the flavor of foods (tin and acidic dishes, for example).  That is why there are often instructions to use non-reactive containers. However, this has nothing to do with the weather.  Of course, ambient conditions, such as extremes in humidity or temperature, can impact the cooking process, when baking, for example...but storms don't accelerate or influence spoilage.