Here is a post from someone on another board (regarding a post about a different well-known brand of soap):
"...my understanding is that as long as you don't mention that your soap has some beneficial quality, i. e., good for acne, etc., it is not considered a "cosmetic", it is "soap", and therefore INCI nomenclature is not required. "
This was tested via our US distributor and the FDA officer concerned
had a different spin on things, and INCI nomenclature was required. We
do not make any claims on our packaging. The response from FDA (the
exact written words from the FDA officer) was:
Soaps that do not contain any cosmetic ingredients such as fragrance
and colors and are purely made of saponified fatty acids are not in
FDA’s jurisdiction.
The only soaps that are not regulated by the FDA are solid bars of
basic unscented soap that have no cosmetic ingredients or claims.
In other words, if you add a fragrance then it becomes a cosmetic.