I sympathise with your sentiment, but I do think you should expect pushback, because such a notion is obviously problematic. I'll just pick a few of the obvious issues:
1 Incompatibility
It is generally not possible to make different values compatible in this way just by splitting off into smaller societies. Values aren't just abstract, they are moral claims about real things. For example, if my value is that I have the right to retain my inherited feudal rights as Duke of Redland, but the serfs of Redland don't agree, we have a problem. It's not just that I want to live in a generic feudal society, it's that I place moral value in the specific history and laws and inheritance rights of Redland, which I view as just and legitimate. So we need some kind of arbitration decision as to which kinds of values get implemented, and which don't. There is nothing stopping communists from setting up their own little communes, and indeed many have. But they also want possession of already existing wealth, which is always going to be contested.
2 Outsiders
I'm living in my little society, you're living in yours, each one reflecting our conflicting values. But our societies still have to interact. Trade, boundary disputes, pollution, migration, whatever else. Whose laws, customs and values should govern our interactions? What's more, external relations are often determinative of a society's success or otherwise, particularly for very small societies. If no-one wants to trade with sub-society A, perhaps they aren't viable. Should everyone else be forced to trade with them, in order to uphold your right? By saying individuals have the right to live in their own society, you are just pushing problems of contention up a level, from intra-society to inter-society.
Also, every society faces constant immigration - i.e. children. Clearly, a two-year-old cannot choose a society that reflects his values. Equally clearly, we are shaped by our experiences. If I wish to live in a closed community that constantly reinforces belief-system B, that is one thing. But if I bring my child up in that community, when he reaches adulthood his belief in B, and his desire to remain in that community, will not be based on surveying all the possible options, but just because it's all he knows.
3 Change
Suppose I want to live in society C. Then I change my mind, and I want to leave. What happens? Alternatively, suppose I want to join society D, but they don't want me. Suppose most people in society E decide that E was a mistake, and want to keep their society together, but change its ways, but the minority disagree.
Ultimately, I worry that your proposition is a way to evade the problems of politics, rather than solve them. If you aren't already aware of the literature, you might be interested in reading about anarcho-capitalism, which is similar to what you're talking about.
As a general point, your counterarguments seem to be based on the idea that "value-based self-organization" of human societies is infeasible. But it can't be that infeasible, since an approximate form of it exists today. The current organization of human society runs up against all the same problems you listed - for example, many Americans feel that the current US government is illegitimate, mirroring the feelings of Redland's serfs against their Duke. Modern countries have to interact on issues of trade, pollution, boundary disputes, etc - and t...
I skipped October and November owing to election season, but opening back up:
As Multiheaded added, "Personal is Political" stuff like gender relations, etc also may belong here.