I combed through the reviews of each of the OT films (Star Wars, ESB, ROTJ) as they were known at each respective release. The reason I'm choosing reviewers is because they were the primary public avenue for gauging reactions. This is going to be a long one.

Starting with the first film, one notices a common trend in 1977 reviews:

"Star Wars" is a fairy tale, a fantasy, a legend, finding its roots in some of our most popular fictions. The golden robot, lion-faced space pilot, and insecure little computer on wheels must have been suggested by the Tin Man, the Cowardly Lion, and the Scarecrow in "The Wizard of Oz." The journey from one end of the galaxy to another is out of countless thousands of space operas. The hardware is from "Flash Gordon" out of "2001: A Space Odyssey," the chivalry is from Robin Hood, the heroes are from Westerns and the villains are a cross between Nazis and sorcerers. "Star Wars" taps the pulp fantasies buried in our memories, and because it's done so brilliantly, it reactivates old thrills, fears, and exhilarations we thought we'd abandoned when we read our last copy of Amazing Stories. - Roger Ebert, Chicago Sun Times.

Ebert's review is far, far from the only one who noticed the strong similarities Star Wars had to Flash Gordon. At the time, most older reviewers like Gary Arnold (Washington Post, 1960-1984) had a certain familiarity with the Flash Gordon and other such references, so they in particular stuck out.

However, I could not for the life of me find many - if any - political commentaries from reviewers aside from the very heavy Nazi / totalitarian influences the Empire sported. Again and again, in the case of the original Star Wars, reviewers focused on the cultural influences Star Wars had. This is something Gene Siskel (future partner of Ebert's, at the time reviewer for the Chicago Sun-Tribune) expresses like thus:

"Star Wars is a battle between good and evil. The bad guys (led by Peter Cushing and an assistant who looks like a black vinyl-coated frog [sic: At this point, the Emperor's role wasn't finalized.] control the universe with their dreaded Death Star.”"

In short, the common theme for Star Wars amongst reviewers was that of a fantasy. Fantasy with cultural and even historical relevance, yes, but still primarily a fantasy. And not a sociopolitical commentary - at least not as its main goal. So as far as the first Star Wars film is concerned, the answer's a big No. It wasn't viewed amongst the most prominent critics as a political treatise per se. Are political elements present? Yes, especially when the Imperials borrow their clothes and organization from the Nazis. But that's more of an element rather than the whole film to the contemporary critics.

As for ESB, there likewise isn't much in terms of purely political commentary. Most reviewers compared the second film to the first - with very different outcomes, ranging from disdain and indifference to high praise. However, there's a catch to it all - which Judith Martin of the Washington Post details:

"The Future is no longer quite pictured as belonging to white males plus one pedestal princess in a white gown. The princess has put on more sensible clothes for wartime, and there is exactly one other woman in the universe, who can be glimpsed working at the home base. There is one black, Billy Dee Williams as a man who seems to have been set up with his own planet by the Small Business Administration and keeps complaining that he has "no choice" about betraying everyone."

With that Star Wars as a franchise takes on a bit more sociopolitical relevance starting with ESB. It may be by an inch according to Martin, but it is still a very notable step when compared to the-soon-to-be-rechristened A New Hope. While this is a rare comment, it is not exactly alone: Pauline Kael of the New Yorker thought that "the big-eared green elf Yoda, with shining ancient eyes, who pontifically instructs Luke in how to grow up wise - Yoda looks like a wonton and talks like a fortune cookie."

I'm going to sidetrack myself a little to add to the point: as it was recieved with about as much variance as 2017's TLJ initially, ESB did recieve a lot of fan complaints too - most of which in fan magazines such as Starlog. One such complaint ties into Judith Martin's observation:

"George Lucas has made a movie even more racist and sexist than the first. I would think that Billy Dee Williams would resent being the token black in the film. Also, there was only one other woman, apart from Carrie Fisher, in the movie."

Thus, the verdict on ESB is that while reviews and reactions of the time didn't focus on the political climate, the expanded cast of characters proved to be ample fodder for sociopolitical discussions. It's hard not to at least see where the fan complaint above's coming from when, again, there are just two women in the film and the sole Black man played a character which came off as villanous - especially without the knowledge that ROTJ would help to redeem Lando.

As such, here we are at ROTJ. To start us off with, I'm returning to the Washington Post and their early Star Wars fan Gary Arnold:

"The cultural impact was even more far-reaching. Lucas succeeded far beyond his expectations at one of the motives behind the project: supplying kids with a fresh source of aspiration. "I saw that kids today don't have any fantasy life the way we had," he said in 1977. "They don't have westerns, they don't have pirate movies, they don't have that stupid serial fantasy life we used to believe in. It wasn't that we really believed in it…but I realized a more destructive element in the culture would be a whole generation of kids growing up without that thing…the fairy tale or the myth…a sort of wholesome, honest vision about the way you want the world to be…

"I had gone around to all the studios with 'Apocalypse Now' for the tenth time and they said, no, no, no. So I took this other project, this children's film."

Perhaps the strangest irony of Lucas' career is that instead of directing "Apocalypse Now," he filmed a science-fiction fantasy that helped close some of the psychological wounds left by the war in Vietnam. "Star Wars" tapped into inspirational depths that transcend political allegiance. It reflected politically uncomplicated yearnings -- to be in the right, to fight on the side of justice against tyranny."

And it is by this point that Star Wars' rampant success had truly crystallized into a massive cultural force. One could see a piece of this with the reactions to ESB - but by the point of ROTJ, Star Wars had spent 6 years in the pop cultural limelight as opposed to "just" 3. Nick Cramp of BBC movies echoes that sentiment:

"The "Star Wars" phenomenon has been seen as timeless modern myth-making; it has also been seen as the triumph of infantilism and a knockout blow to serious film-making. Whatever the verdict, "Return of the Jedi" is a fitting climax to the most successful space adventure of all time."

So to give an answer as to ROTJ: Again, there are no real political allusions aside from Star Wars' cultural impact on past events like the Vietnam War. It should be noted that the War was still very fresh in the public concious, even at ROTJ's release; the War ended in 1975, same year as fellow blockbuster Jaws came out in theathers and 2/5/8 years before each respective Star Wars film. So Arnold's conclusion had sociopolitical relevance.

And to give a final answer: while the parallels may not have been there per se, Star Wars' rampant success meant the franchise garnered very strong reactions from the onset. And reviews slowly but surely took on more and more sociopolitical themes with each film. They may not have dealt with the current political ideas of the then-present per se, but the franchise still touched on may social, cultural and even political aspects.

Sources will be reffered to on request.

I'm going to jump in here with a couple of contextual elements on the creative and narrative side (since u/SKX31 has already given a really lovely answer to your actual question) and an answer to some of the follow-up questions you asked:

I've seen some people put forth the idea that the Rebels were representative of the Viet Cong, which would cast the Empire as the U.S. I'm not sure I agree with that interpretation, but it's one I've seen tossed around.

Lucas has stated that he based the Battle of Endor (and specifically the way the Rebellion and Ewoks won against the Imperial forces) on the Vietnam War, but it was more the Viet Cong's tactics he was referring to rather than the group itself:

Lucas establishes his interpretation of the Ewoks in contrast to the empire at about the 1:03:00 mark of Return the Jedi (chapter 22): “I needed to come up with a primitive creature that was still using sticks and stones and spears--or weapons--and that lived in a primitive society that would be forced to take on the highly technological Empire.” In chapter 29 at about the 1:26:00 mark he remarks, "See, this film was written during the Vietnam War where a small group of ill-equipped people were able to overcome a mighty power.” This comment plays over a scene of the Rebel strike team doing some reconnaissance.

Lucas continues, “It’s not a new idea. Attila the Hun was able to overrun the Roman Empire. The American colonies were able to overrun the British. And it’s always the same story. The Roman Empire had huge mechanical and training advantage over the Huns, but the Huns were still able to overwhelm them with enthusiasm and their human-ness and their belief if what they were doing. And that was the main theme for the overall downfall of the empire--that it was basically overcome by humanity in the form of cute little teddy bears." He makes a similar comment around the 1:46:00 mark in chapter 38: “…the story really is of a primitive society--apparently a weak society--who is able to overcome a very technological society.” Lucas here is speaking over scenes of the Ewoks using rocks and ropes to defeat imperial forces. [x]

The difference lies in the U.S. comparison; while the complex politics and details of the occupation of various planets (and the story of the Original Trilogy) are most certainly based more on other historical times/events, including the Roman Empire and the Vietnam War (with Richard Nixon explicitly being named as the original inspiration for the Emperor, something that I genuinely find hilarious), there are more than enough unique and explicit allusions/shout-outs/parallels, both in-universe and through Lucas' commentary, to indicate that the Empire is a regime that is explicitly based on Nazi Germany rather than the United States (something that, as you already read via SKX31, critics actually did take notice of and talk about).

The original trilogy takes big, grand, sweeping philosophies and applies them in a very vague fashion: with the Empire inspired principally by Nazi Germany (with some contemporary American political issues thrown into the mix), the Rebellion (and by extension, the Ewoks) serve as a stand-in for your everyman guerrilla warfare/rebellion movement. It is the Viet Cong, but it is also the French Resistance and the Polish Home Army and the SOE and every other big WWII-era resistance movement.

When you look at Star Wars (especially looking at Episodes I-VI as a single story), what you're looking at is a story with political and historical basis on an amalgamation of events: there is no single inspiration or basis for the failing Republic and eventual Empire (with Nazi Germany, the Roman Empire, and Bush-era America being the three most obvious examples), and there are several other historical people (Napoleon, Ceasar, Nixon, Stalin, Bush), groups (Viet Cong, Knights Templar, Tibetan monks), and regimes/events (the Roman Empire, Vietnam War, the Cold War, the War on Terror/Iraq War) thrown in there too; the deliberate parallels and callbacks to Nazi Germany are simply the most explicit.

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