According to theBREASTFEEDING ANSWER BOOK, published by La Leche League International, no evidence exists that the nursing mother's use of hair-care products, such as hair dyes and permanents, has any effect on her breastfeeding baby. When a mother uses hair-care products, some of the chemicals will be absorbed through her skin. If her scalp is healthy and intact, less will be absorbed than if the skin on her scalp is scratched or abraded.
The BREASTFEEDING ANSWER BOOK, 3rd revised edition, states on page 449, "No evidence exists that the nursing mother's use of tanning beds has any effect on her breastfed baby."