Your skin is an incredible organ evolved to keep out toxins that your digestive system must remain vulnerable to if it is to continue doing its job.  I believe this is why smell has evolved to be such a good/necessary indicator of what is acceptable for the digestive system.  However, evolution takes time so I understand your concerns.

How do you feel about sunscreen?

Personally I only use deodorant and not antiperspirant.  I use SpeedStick or sometimes just spray the pits with cologne.