"May contain traces of milk." Hundreds of products in our database carry a line like this: 795 of them matter for a vegan check and 308 for gluten. It is probably the least understood sentence on any food label, because it does not mean what most people assume.
It is not a measurement
In the EU and UK, precautionary allergen labelling is voluntary. There is no legal threshold a product must exceed before writing it, and no requirement to write it at all. One factory prints "may contain" out of caution on a spotless line. Another skips it despite real cross-contact. The presence of the warning tells you the company chose to warn. The absence tells you nothing.
So how should you read it?
For allergy, take it seriously. Cross-contact amounts can be small, but allergic reactions do not read statistics. If milk or gluten sends you to a hospital, a traces warning is a real signal and certified-free products are the safer bet.
For ethical veganism, it is a personal call. No animal ingredient was added to the recipe. Most vegans accept trace cross-contact as a fact of shared factories, and campaigning groups generally agree that avoiding such products does not help any animal. But it is your line to draw, not ours.
For religious dietary law, ask your authority. Rulings on trace amounts differ between schools and certifiers. A certification logo resolves what a traces line cannot.
What we do with it
We show the warning, separately from the verdict, and we do not silently downgrade a product for it. A cookie with clean ingredients and a milk traces line gets its warning displayed next to the answer, so the person with the allergy and the person with the ethics can each make their own decision from the same page. Flattening that difference into one verdict would be lying to one of them.