"But what if to do nothing was to support the existing state?"
the idea that "doing anything is better than doing nothing" is severely flawed imo. voting is one thing many people "do", and i'd say that is worse than doing nothing, especially in terms of supporting a state. and then, what does one mean by "do nothing"? the impact of one's actions on the existence (and strength) of a state is usually negligible at best.
"Wouldn't that be support of oppression by a state on people who no longer want to be a part of it?"
it is up to the people who no longer want to be a part of it, to figure out how to change their lives so that they are no longer part of it, or at least minimizing their part in it. if bringing down the state is the only option they can see, i wish them luck. but we all know how successful that has ever been. meanwhile, individuals (including groups of friends/comrades/allies) can choose to live differently - in ways that minimize the impact of the state on their own lives.
i reject the activist/liberal concept of representing the "oppressed" and acting on their behalf. we are all oppressed (to varying degrees), and it is up to each of us to fight that oppression in whatever ways we choose. including gathering allies when it makes sense.
here's to unmediated life and relationships! fuck states and every other abstracted system of power and control.