Fermented and still-alive stuff on the trail would be tough... While still alive, Kombucha would be most stable if there was no more sugar for digestion. However, this means it'd be more acidic and/or alcoholic than most people would want.
Wish I had more ideas for living probiotics for the trail. Is miso powder active again, once rehydrated? (Paste miso shouldn't be exposed to boiling water, as it's alive.) Various alcohol brews would be stable enough for packing. Oh, and "old" Alaskans are called "sourdoughs" for a reason.
On a related but different note, there are possibilities for sprouting while hiking.