A nomad base doesn’t need to follow any certain political direction but the idea of sharing a space with lots of people does tend to create a certain type of anarchy/communism to prevail. Giving up ideas of private property was the best way to manage everything. With dumpster diving this is easy to do as the food is not being paid for by anyone and so doesn’t have some legal ownership anyway. This encourages the gift economy too as there is no point in buying something for yourself in the nomad base as everyone is going to want to use it. So you might as well just gift it to the nomad base and let everyone use it anyway.
But there are personal items which have either sentimental value or economic value useful for work purposes. These should be respected as such and this doesn’t go against the principle of no private property but are part of the commons that enable the space. For example a laptop that is used to work on to pay the rent is better to be looked after by the person who does that work and therefore ensure the long term sustainability of the place rather than have it used by someone who might potentially destroy the working environment and cut off the income source. But things like musical instruments can be great to share with everyone as talented musicians can bring pleasure to everyone without having to own an instrument if there is a collective one that everyone can use.
Most importantly the idea of having no private property means that everyone cares about everything. If something breaks it is up to everyone to fix it. Having fixing and cleaning times can be a good team bonding activity. There is something really nice about everyone helping to fix the broken bicycle and get it running again, or when magically the entire base gets cleaned in only an hour because everyone helped do a little bit of something. By not having responsibility fall back on the owner of everything the delegation of tasks become a community issue and removes all leaders and hierarchy as well.