It can be argued that most of Science Fiction has at least some sort of political background and relevance, but what I'm really looking for is stories where the political aspect is central to the story, not just decoration. So based on the list of sub-genres from the precious post, I have selected the following as those most relevant, ordered according to the importance political thought plays in the overall sub-genre:
1. Dystopia / Utopia
2. Soft / sociological science fiction
3. Alternate history
4. Apocalyptic, holocaust, and post-apocalyptic
5. Near-future science fiction
8. Military science fiction
Dystopia is at the top of the list, and paired with its counterpart Utopia, because the very essence of the sub-genre is socio-political conflict. The character in Dystopian stories are just a view point for a run down, bleak society; Orwell's 1984 is told from the viewpoint of Winston Smith, Fahrenheit 451 is told from the viewpoint of Guy Montag; The Handmaiden's Tale is told from the viewpoint of Offred. The same can be said about Utopia, the relevant aspects are in the society and not the characters. Subsequent posts will deal more extensively on this issue.
Soft / sociological science fiction is less straightforward in this regard, for many of the stories center completely on the development of the character, with the social background an excuse for the specifics of said development, as is the case with Ursula K. Le Guin's The Left Hand of Darkness; there are also other stories where character development, while still important, are not as strong as the socio-political background they're set in, and once more the best example comes from Le Guin, but this time on The Dispossessed.
As I have said before all other sub-genres might contain elements of political background, and even though I have also said that Alternate History is not entirely SF, I have included it in this list because when the works are Science Fiction they tend to have a focus on the socio-political aspects of this alternate reality they speak of.
The next on the list is Apocalyptic, holocaust, and post-apocalyptic SF. More often than not these stories have an action/adventure plot, with the Apocalypse as landscaping, like in Frederik Pohl's Wolfbane, but more often than not you can catch glimpses of the social, and therefore political, structure emerging from the catastrophe, and in some cases, such as Lucifer's Hammer by Larry Niven and Jerry Pournelle the action scenes are a result of the new social order emerging in the midst of the chaos.
In order to keep these posts to a reasonably user friendly size I have decided to break this one up, so wait for the second part for the other politically relevant sub-genres. And once more if you agree or disagree with any of the things I said here please let me know.