Cringe all you want, the reference is there from the start.
The first episode in which Romulans appeared was TOS: "Balance of Terror" - This title is a direct reference to the Cold War arms race between the USA and the Soviet Union. The phrase was coined by Lester Pearson in June 1955, "the balance of terror has replaced the balance of power," at the 10th anniversary of the signing of the UN Charter.
The third episode in which they appear ("The Enterprise Incident") is again a pretty obvious play on US/Soviet Cold War spy games.
Anyone who doesn't compare the Romulans to the Soviets, to my mind, has failed to remember the historical context in which TOS was written.
In later portrayals, the "Tal Shiar" secret police are a pretty obvious analog of the real-world KGB. The Soviet Union reference was still alive, as Next Gen started airing in 1987, but the Soviet Union didn't fully dissolve until 1991. The tension between the Tal Shiar and the Romulan Military roughly mirrors what was going on in the Gorbachev-led USSR...
By the time DS9 rolls around, the Romulans have again followed the Soviet/Russian progression, and have become sometimes allies, sometimes adversaries in a politically complex world without clear superpowers.