So while using a cream containing triethanolamine may not be able to "give you" cancer, when you also use a dozen other toxic products, and eat crops sprayed with innumerable chemicals, and drink a few dozen more in your water, and inhale car exhaust on the way to work, the sum effect may in the end result in cancer, especially if your mental state inclines you to this kind of pathology (see the science of psycho-neuro-endocrine-immunology) which is why the more new chemicals mankind produces, the more cancers occur (currently rising at a rate of 1% per year since at least 1960).
So take care, make your own decisions, and if you feel strongly about it, vote with your money for the world you want.
I couldn't agree more. – Because it is indeed very difficult to gauge just how the proliferation of chemicals affect our bodies, it seems to make sense to cut out what you can; but there's no point being paranoid: we can barely avoid exhaust fumes, chemicals in the office carpet, whatever finds its way into the water we drink and the food we eat (even if it's organic). Find your comfort level: I avoid parabens etc. wherever I can - and there are so many excellent products which make it easy - but that doesn't mean I won't use anyone else's soap to wash my hands with, when the need arises. And I do like the smell of Proraso...