Regarding soaps.
An ingredient can cause an immediate reaction in the form of a primary irritation, which would effect anyone using the product. Alternatively, it can cause an allergic reaction in those persons sensitized to the particular ingredient.... Synthetic additives are not alone in precipating negative reactions...,. Even natural essential oils used in old recipies can cause problems. Among potential photosensitizers are oils of bergamont, cedar, coriander, lemongrass, orris root, orange, parsley and yarrow, ... Cocoa butter and coconut oil may produce a reaction in those allergic to chocolate and nuts.  Natural emollients such as lanolin and glycerine are also culprits. Honey if allergy to pollen.

Benzoic acid found in ....margarine, cosmetics, skins salves, and soaps can cause possible skin rashes.
Bergamot oil ...possible ecxema
Camphor... skin rashes
Patchouli.. possible allergic reaction
just a few problems that are known with essential oils.

Photosensitizers cause the skin to react when exposed to light.

and we didn't mention colorants yet.

The Art of Soap Making Marilyn Mohr