Polyester cycling wear gets stinky because it encourages bacteria under the arms to reproduce. It's the bacteria that smells by the end of the day. Polyester is the worst thing to wear if you want to avoid smelling.

The new soft fine merino wool apparel does not itch against the skin. It's soft and lovely feeling. Three major sources to buy it from are Smartwool and Ibex and Icebreaker. People just don't get the fact that it's not heavy and itchy until they try one on and see for themselves. Merino wool breathes, and bacteria do not like wool and hence you can wear wool for days and not smell much underarm aroma. A thin merino top will keep you warm when it's cool out, and also it will keep you from getting clammy and sweaty when it's warm out, because it breathes. I plan to wear some thin merino wool tank tops this summer. It just feels GOOD, and unlike polyester it breathes, and it does not smell. Plus, you don't have to wash it nearly as often as polyester.
Merino wool....it's not like your grandma's sweaters anymore.

I use that crystal deodorant as well. It's basically just mineral salts and inhibits bacteria growth under the arms. I like using it much better than some strong anti-perspirant.
I would just make one comment in addition- I have known some people who don't use deodorant in order to be 'natural' and they bathe every day. But they sweat and they do smell. They smell from 2 feet away and it's not the most pleasant thing to talk with them. But- they do not smell themselves- they have become accustomed to their own underarm smell and do not think it is noticeable by others. I know this because I have heard them state that they don't use deodorant and they don't smell. But they do smell. Mind you, I don't think a healthy underarm odor is anything bad per se, a mild clean underarm odor can be appealing in fact....but as a society we are just not used to it, plus I have observed that manmade fabrics such as polyester makes this smell much worse.

I think if you want to go with the no deodorant lifestyle you really should at least stay away from man made fabrics. Stick to natural fibers that breathe.
"Wicking" claims from polyester promoters are a poor substitute for the natural wicking properties of wool. Just my opinion. I own polyester items and use them for certain purposes...but mostly as bottoms/tights and as tops but not against my skin where they will always start smelling bad. When I wear wool (or linen/cotton) I don't have that problem at all.