Rinat Enikeev
Politics is how collective actions are customarily carried out in a given community. Political thinking is a complex of ideas and evaluations concerning politics. Libertarian political thinking is political thinking determined by libertarian principles. The culture of libertarian political thinking is how it is reproduced and promoted.
Now the full definition: the culture of libertarian political thinking is how the complex of ideas and evaluations regarding how collective actions are customarily carried out in society, determined by libertarian principles, is reproduced and promoted. How is this culture structured?
In modern society, politics very rarely corresponds to libertarian principles, so a libertarian usually involuntarily shuns politics. In what cases will they not shun it?
First, the collective action must be voluntary for its participants. Rallies by quota, mandatory elections, and the like will be sabotaged by a libertarian whenever possible.
Second, the collective action must pursue an obvious benefit for its participants. A libertarian is unlikely to be inclined to pull chestnuts out of the fire for others.
Third, collective action may involve causing harm only if it is intended to restore justice. Lynching or street clashes with police committing illegal acts may well fit into libertarian political thinking. Pogroms—unlikely.
How are all these values reproduced and promoted? Like many other cultural ideas: through personal example, references to successful political actions, and campaigning.