I have to admit that beyond the general concept, my last in-depth contact with T2K was in the 1990's playing the pen and paper version, and a brief reunion with the highly ambitious but spectacularly failing computer adaptation*, so my memories might be hazy.
I had heard that they tried to modernize the backstory or keep inventing reasons why the Soviet Union did not collapse or make a comeback (even briefly considered backing the 4th edition Kickstarter for nostalgia kicks), but personally, I think that a post-nuclear game is so deeply tied to the Cold War that the developers should just have kept it as an alternate universe. Or now that the year 2000 is farther in the past than it was in the future in the 1980's, why not go full retro and have the setting as "Twilight: 1985"?
That said, I bothered to google and apparently even the original game needed an outlandish plot to trigger The War where a cabal of East and West German officers stages a joint coup against the Soviet troops in East Germany, whereas a simple accident or a single incident escalating out of hand would have been more plausible (and more likely) alternatives. That WW3 was averted at all was either a testament to the good in human beings or just sheer dumb luck, or a combination of both. (And then I ran into the background for the third edition and sighed deeply. Either it was meant to be an outlandish prank, or, well, I don't know.)
But like said, the real attraction of T2K is to set the tried and true tropes of "fantasy adventurers versus an evil overlord" or "frontier pioneers are harassed by bandits, cavalry to the rescue!" in the modern age. Balancing between making the world devastated enough to allow this to happen, but not so devastated that nothing matters anymore because everyone is going to die two weeks from now anyway, well, that is certainly difficult.
Regarding the relations between the local civilians and the adventuring party, one could argue that the survivors are so jaded that they don't care anymore who was fighting whom before the bombs went off, or who exactly fired that theater ballistic missile at the nearest town, it's enough that if the latest armed arrivals are NOT arriving as oppressors or raiders but willing to sell their services to the community which might help them to survive to another day. Plus this being the nuclear war and whatever author's fiat brought NATO troops to Poland, one can be sure that the West was not the only one to drop nukes on Poland in such a scenario. (Acccording to now-declassified war plans, "sunshine from both directions at once" was actually in the cards for Finland even before the War would have gone nuclear between NATO and Warsaw Pact. So much for "credible neutrality".)
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*) It was entirely possible to find in the post-nuclear Polish countryside someone who was supposedly a key person in the local resistance against the Evil Overlord, yet only spoke French, or Estonian, or Azeri - yes, the only language a key NPC to advance the plot halfway through the game spoke was randomly selected from the pool of the 30 or so languages characters could be given as background skills, and loading a saved game didn't help because the selection had been randomized at the beginning of the campaign: if you hadn't chosen the right language in the beginning of the game, you had to restart the game from beginning or use a hex editor to alter your save files. This being before everything was on the Internet, I started over, taking care to include in the party a couple of throwaway characters who spoke all the possible languages, then breezed my way through using all intended or most likely unintended exploits of the game I had already discovered while playing. Was it worth it? Not in the slightest. There was less and less narrative and cutscenes the farther the game went on, and finally it ended in a congratulatory text screen, including a blurb for (never released) Twilight: 2001 set in the ruins of the US, as if I or anyone else who bought or copied the game had wanted any more of the same.