I mean, I wouldn't let my cat eat a stick of deoderant or lick my armpits haha, but if you had deoderant on and like snuggled the cat under your arm I wouldn't think it's a huge problem - I'd brush out the cat and/or wipe him down with a damp cloth... if for some reason your cat got into a stick of deoderant and started to eat it, I'd take him into the vet
I can't imagine its good for them but I'm sure if they don't eat it, then they'll be fine. Since your talking about hygiene products, beware of dental floss. A friend of mine had a piece of dental floss in her bathroom and somehow her cat got a hold it and ate it. This caused the floss to rap around the cat's stomach parts and unfortunately killed him. Just a warning though..