It was one of the "bad" episodes, which leads me to believe it was from the third season. Yangs (Yankees) Kohms (Communists) and they worship an American Flag...talk about beating us over the head with an idea.
Let That Be Your Last Battlefield was the one with the half white, half black guys fighting each other because of race, essentially, IIRC. I actually like that one. It's another case of Star Trek pumelling you with the message they're trying to get across, but at least it's not a nationalistic one.
Perhaps true, and I'm watching it from a different perspective, having not been alive in the 60s, but it always struck me as saying, "These ideals are the ones to live by and the only place to find them in the universe is a place that comes from a parallel America."
It was far-fetched to me, even more so than the planet that was a modern version of ancient Rome.