At least with me after a few days everything stinks with or without anti microbial!
To be a little more specific, the stink I am referring to in this case is the one
that settles into the fabric after a while and even after washing it is still somewhat
present. This was especially true with my Patagonia's Capilene for example, but has
never been an issue with the wool shirts (Ibex and Icebreaker) that I have used for
several years now.