Nearly all allergens are proteins. If I'm not wrong, it's because proteins are the main form of biological effectors. For instance, a cell makes all sorts of signalling proteins (neurotransmitters, hormones, enzymes, etc) that bind to the receptor of other cells.

How does the receptor distinguish between different types of signalling proteins then? It's the protein's shape. So proteins have all sorts of shapes, with one shape for one receptor.

Whereas carbs and fats are mainly used as energy, not to elicit a biological functions. So carbs and fats come with less diverse molecular shapes.

Coming to the immune cells. Immune cells have many receptors that recognize foreign protein shapes. So if one of the immune cell's receptor fits with a food protein by chance, then food allergy happens.