Cross-contamination is always a risk in shared factories, hence why “May contain” needs to exist - they’re listing known allergens the factory is handling. The vegan / vegetarian labelling supports a dietary choice rather than allergy advise.

As the article highlights, “free-from” labelling has more stringent controls and requirements to eliminate cross-contamination. The “free-from” products labels people should be seeking if they require it to be allergen-free.