The carcinogen in question is 1,4 Dioxane (also known as just dioxane and not to be confused with dioxin). According to the Organic Consumers' Association, dioxane is in Avalon Organics Nourishing Shampoo and in Glycerin Hand Soap. I'm not sure why California singled out Avalon; dioxane crops up in all sorts of products (mostly shampoos and soaps, since dioxane is a foaming agent), including baby care. I've posted a link to the Organic Consumers' Association (OCA) at the end, in case you want to check out the list.
My Method dish soap will have to bite the dust. But how worried should we be about dioxane? According to the California Environmental Protection Agency, dioxane is a neuro, kidney and respiratory toxin. It is a known carcinogen for animals: rats given it in their drinking water developed liver cancer. Several workers have died as a result of accidental exposure to it. In these cases, exposure was to a very high level.
Worryingly, it is a veritable silent killer: you won't ever see dioxane on a product label. Dioxane is not an ingredient at all, it is a by-product of a process called ethoxylation and so could crop up in synthetic ingredients that have been through this process. According to the OCA, these include myreth, oleth, laureth (in a fact any thing ending in eth), PEGs, polyethelenes and anything with oxynol in its name.
If, as I did, you suspect that the OCA might be exaggerating a tad, then check out the Agency for Toxic Substances and Disease Registry.
It acknowledges that dioxane has given animals cancer in studies and this is what it says about cosmetics and dioxane:
"1,4-Dioxane may be a contaminant in cosmetics, detergents, and shampoos that contain the following ingredients (which may be listed on the product label): “PEG,” “polyethylene,” “polyethylene glycol,” “polyoxyethylene,” “polyethoxyethylene,” or “polyoxynolethylene.” Many products on the market today contain 1,4-dioxane in very small amounts. However, some cosmetics, detergents, and shampoos may contain 1,4-dioxane at levels higher than recommended by the FDA for other products."