1967 - “A Taste of Armageddon”: Captain Kirk introduces the technocratic elites of rival worlds to the full horrors of warfare. Totally apolitical.
1968 - “A Private Little War”: Superpowers fight a destructive proxy war on a jungle planet; aired during the Tet Offensive. No politics here.
1969 - “Let This Be Your Last Battlefield”: White-and-black guys oppress black-and-white guys until their planet is destroyed in a race war. Aired 9 months after Martin Luther King Jr. was assassinated. Politics-free.
1986 - “Star Trek IV: The Voyage Home”: In this apolitical adventure, the crew of the Enterprise travels back in time to the 20th century to rescue humpbacked whales from extinction at the hands of industrial over-fishing.
1987 - 1994 - “Star Trek: The Next Generation”: Set in a post-scarcity communist utopia in which profit motive is looked upon as barbarous. Debuted during the Reagan Administration. Just a mindless adventure series.
1991 - “Star Trek VI: The Undiscovered Country”: Two superpowers negotiate an end to their decades-long Cold War over the objections of reactionary factions in both countries. Aired 4 months after the attempted coup against Gorbachev and two weeks before the dissolution of the USSR. No politics here.
1992 - “The Outcast”: The Enterprise visits a planet with only one biological sex, where a character who nevertheless identifies as a woman is forced to undergo conversion therapy. Released at the height of the AIDS epidemic. Mercifully free of politics.
1993 - 1999 - “Star Trek: Deep Space Nine”: This politics-devoid series, which coincidentally aired during the Balkan Wars, follows a group of Federation observers who are assigned to guide the recovery of a war-torn planet.
1995 - “Past Tense, Parts 1 and 2″: Sisko, Bashir, and Dax take an apolitical trip back in time to an austerity- and inequality-ravaged early-twenty-first-century America on the cusp of revolutionary class violence, where despairing poor people are locked in ghettos whilst they “look for work”.
1996 - “Bar Association”: The employees of Quark’s Bar strike against exploitation by their employer; Rom literally quotes Karl Marx to his brother (in a wholly apolitical fashion).
2000 - “Critical Care”: The Doctor is abducted and forced to work in a horrifying, dystopian hospital where quality care and competent medics are reserved for the rich and well-to-do whilst the poor are left to bleed in an over-crowded, septic, dingy little room. Any resemblance to the American healthcare system is purely coincidental.
2001 - “Repentence”: Voyager finds itself needing to escort a bunch of alien deathrow prisoners to their execution, but finds that there is an entirely apolitical racial bias in who gets sentences in this fashion, and also that many of the murderers are not beyond reform.
2001: “Broken Bow”: Airing three weeks after 9/11, this apolitical episode finds Starfleet in conflict with a cabal of terrorists known as the Taliban Suliban.
2004: “The Forge”, “Awakening”, and “Kir’Shara”: A corrupt Vulcan government cracks down on pacifist dissidents and tries to instigate a war against with Andoria through bogus accusations that they are developing weapons of mass destruction. Aired in that lovely, politics-free aftermath of the US invasion of Iraq.