The H412 comes from sodium laureth sulfate (SLES) which is contained (in large amounts, like 20 to 70% by weight) in practically every kind of liquid soapy detergent, shampoo, liquid hand soap and what not. The only reason you know of that one product is that they seem to sell to professionals as well, which is why they need a material safety data sheet. Your shampoo doesn't need that, so you just don't know that it is just as harmful.

Edit: Dawn seems to contain it as well, look for CAS# 68585-34-2: https://msdsdigital.com/system/files/Dawn_Professional_Dish_... The missing H- and S-numbers in that datasheet come from the differing standards and maybe the different concentrations.