Vegan labelling has nothing directly to do with allergens. What we mean is that allergens are not even factored into whether a product is vegan or not. Yes, whilst some allergens are animal derived, it is not the allergen risk that is considered when determining the vegan status of a product.
For example, whenever a product is made on the same equipment as an allergen, there is always going to be a small risk that a trace of that allergen could remain from being missed in the cleaning process. Provided that the manufacturer is using what is called GMP (Good Manufacturing Process), the risk should remain very low. So low in fact that it will not affect the vegan status of a product. However, if you have a severe allergy to a specific animal derived ingredient such as dairy or egg, you should not rely on vegan labelling to determine if a product is suitable for you are not. For those at risk of severe allergic reactions, we would recommend that you visit the Allergy & Anaphylaxis Australia website here for further advice:
If a batch of a product that is labelled as vegan is discovered to accidently contain a trace amount of milk through testing done by the manufacturer or relevent state/territory authority, the manufacturer will likely issue a recall on the product. If you are vegan but not allergic to milk, then you may feel gross that you might have accidently eaten animal ingredients, even if only a tiny amount, but that is entirely different that you may die from eating that trace amount of milk because you have a severe milk allergy. For example, your allergy is so severe that you have to carry an EpiPen around with you everwhere.
It is also worth noting that Precautionary Allergen Labelling statements such as “may contain….” are voluntary and not required under the current Australia New Zealand Food Standards Code. This means that even if you do not see a “may contain” statement on a product label, you should not assume that the product is fully allergen free. You should contact the manufacturer directly to ask about the risk of any particular allergen.