I am sitting here looking at the list of ingredients of an underarm deoderant which includes propylene glycol, sodium stearate, stearyl alcohol, and a yellow and  blue dye. These don’t sound like foods to me. If they are not foods, then there must be chemicals that if absorbed into the body (or ingested), then the liver is obliged to detoxify them for excretion by the bowel or kidneys.
For years we have considered our skin to be this impenetrable covering for our body. But is this really the case? I started to think about this when I realized how many drugs are now being delivered via the skin. If we can put on a patch and have a medication delivered to us through our skin, just how impermeable is our skin and how safe is it to put various things on our skin that we would not dream of eating?
For a long time, I did not have a good alternative to underarm deodorants. Then at a Nutritional Meeting I heard a woman speak about the subject and to say that she  used baking soda. I have used it for the past several years and can give you a few comments. First, it needs to be dusted on the arm pits daily. It will not last beyond 24 hours. Second, I have had to use small containers of baking soda to use in by dop kit.
I believe this concept expends well beyond underarm deodorants. Face and hand creams, lip gloss are some things that come to mind. Look at ingredients. The more strange sounding components they have, the less likely I am to buy it.
I think that as a general rule, the fewer toxins we present to our liver to be detoxified, the less risk of   cancer we will have, and the healthier we will be.