I'm slightly confused regarding yr precise query so i have noted my interpretation of yr OP. maybe it's just me that's confused.
i deduce that the food packaging section can be ignored within the context of yr question since zero possible interaction with non-food section. OK.
I deduce yr query only relates to products run in the Non-food section.
Is yr query then some /all of -
(a) whether soap (eg product A) which contains a dairy ingredient (milk) must declare the presence of dairy allergens on the label ?
(b) whether other non-food items processed after A require the shared line/environment to be cleaned/sanitised and validated free of dairy allergen. Or perhaps appropriately labelled, eg "may contain dairy allergen" ?
© whether, as per MM's post, any regulations exist regarding potential cross-contamination of "other (??) kinds" between non-food products using shared-line, etc and related, required, measures of avoidance.
Personally i have no idea to (a,b,c) but for USA the regulatory answers are (maybe partly) within here -
I could not find any mention of the word "allergen" in above link. As in foods, Adulteration appears a popular US strategy.
Have attached a recent UK based, allergen oriented, survey of some eclectic non-foods (including cosmetics, personal care [soaps et al], medicines and condoms). The text implied (to me) that, in the present context, regulations/labelling requirements are mostly rare, often non-existent.
Non-food allergen problems.pdf 299.12KB
Rgds / Charles.C