See page 105 of Soap & Cosmetic Labeling by Marie Gale, regarding Incidental ingredients. And if you don't have that book, then look here:The implications of that would be huge. With all the misinformation on the internet, I would love to see a citation of that. Can you provide a link of some sort to a credible source? Thanks!
https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfcfr/CFRSearch.cfm?fr=101.100
https://www.fda.gov/Cosmetics/Labeling/Regulations/ucm126444.htm
https://www.fda.gov/Cosmetics/Labeling/Regulations/ucm126444.htm#clgl9
The above are for the US, and the US only. So for the EU and some other countries, other regulations may be more or less stringent. Even within the US, some state regulations are more stringent than the federal regulations, Florida and California, for example. One has to comply with the most stringent regulations for the locations in which one manufactures and sells. In my opinion, once someone starts selling internationally, the labeling requirements become that much more complicated.
N.B. I just learned something new regarding my current state. There is a requirement that any product containing lead must contain a warning regarding lead poisoning dangers. That lead me to wonder if the red oxide I use contains lead. Well, unfortunately, I don't know, but it could, making it illegal for me to even give this soap away in the state of Illinois without said warning on the label! This is huge for me because, even though I don't expect anyone to eat my soap, soap eating is a thing that I have to take into account when labeling soap.
https://nvlpubs.nist.gov/nistpubs/ir/2017/NIST.IR.8178.pdf