My DD had a coconut allergy she outgrew and past a challenge in February 2015. She originally tested positive for the allergy and a couple years later had a reaction to accidental coconut ingestion.
When I first started, we stuck to Kiss My Face olive oil based products and soaps made from goats milk. (we also had to avoid Shea Nut which limited us as well)
I am not a doctor. I am a mom with a child who was allergic to coconut and this is what worked for us.
There are more soaps out there that you can use if your kiddo is not allergic to man made coconut products. Way back when I started researching coconut I called a company, might have been Johnson and Johnson, and somehow got lucky enough to speak with a chemist! Super fantastic guy who spent so much time on the phone with me talking about coconut.
There are different man made coconut products and how much coconut protein then have in them depends on the formulas and raw products they manufacturer uses.
His advice that I followed was:
Avoid: Cocamide DEA, or cocamide diethanolamine and Cocamide Mea, or cocamide monoethanolamine
Patch test first - and or discuss with your allergist: try using products containing Cocamidopropyl betaine as this product is so processed that there is little or no coconut protein left.
My daughter had no issues using products that contained Cocamidopropyl Betaine and it opened a world or products for her as she got older and it began to matter to her what shampoos and soaps she was using. She did not like the smell of the Kiss My Face soaps.
It is appropriate that coconuts be considered a tree nut because other tree nuts are in the same botanical family. Coconut is a drupe. If you do a Google search you will find may sites that explain the difference between a true tree nut and a drupe. My favorite site for this is:
http://waynesword.palomar.edu/ecoph8.htm. There are very few actual tree nuts. You will find "nuts" like almonds, pecans, and macadamia nuts to actually be drupes like coconut.
It was a huge help to us when the FDA added coconut to the Tree Nut category for food allergen disclosure.
Feel free to pm me if you have questions I can help answer.