i hope to say some more, but as a placeholder for now.....
i like to think about how mutual aid/gift economy would work in capitalism, the condition i live in now. and then i like to live it as much as possible - reducing my experiences of monetized relationships and capitalism, and expanding my relationships involved in gift giving/receiving and mutual aid.
i have no illusions of changing "society", but the more i move my life from the realm of monetary transactions to one of relationships based on receiving and giving freely, the more satisfied i feel, the more intimate my contact with humans, other creatures, and the earth.
when i eat the salmon my neighbor caught and gave to me because they wanted to, an entirely different chain of events, relationships, and feelings take place than if i'd bought a piece of salmon under shrink-wrap from a store (which perpetuates many more monetized relationships beyond my own purchase of it, both before and after the actual sale - not to mention it doesn't taste as good, nor do i feel the same sense of gratitude). when i split the fallen manzanita tree on my neighbor's land into firewood for her rather than her paying someone to chop it or paying a business to deliver wood (that perhaps they paid someone else for trees grown and cut down somewhere else), the same sort of changes occur. or when someone who lives near me organized an open mic where people played music together (or listened to those playing) rather than paying for "entertainment". or when a couchsurfer stays a night in my home (without money involved) rather than booking a hotel room, or i stay at their home during my travels.
so in that respect, "society" does change to a degree when living with a mindset of mutual aid. but my primary motivation for living that way comes from the experience itself, and the desire to expand those experiences and relationships in my own life.