Compare our invasion of Korea with that of Vietnam only a few years later. Before you say "Korea was UN-approved" — no, that's a lame excuse. Stalin boycotted UN at the time action on Korea was decided, but by the time of Vietnam USSR has changed its approach. That's all.
So what? You're talking about the public perception of the war, UN approval forms part of that public perception.
In both cases American military was sent to fight in remote lands against people, who didn't threaten America directly in any way — for fear of the domino effect of Communism. In both cases the fighting was heavy and numerous war-crimes have taken place.
And yet, there was no domestic opposition to the Korean war — virtually none. No protests against the draft, no accusations of returning soldiers being "baby-killers". John Kerry, for example, has gained more political capital for opposing the war (and returning his medals), than for fighting in it (for an entire 4 months).
Vietnam was widely considered a national shame long before the war was lost. Meanwhile the only source of any negativity about the Korean war in mass culture was the M*A*S*H series.
Why was the domestic reaction to the two wars so drastically different? The theory of propagandists controlled and funded (with or without their own knowledge) by the USSR would explain the known facts.
It's possible, but a far more likely factor is the fact they were very different wars at very different times.
The Korean war was over in 3 years. In Vietnam the US stepped into a long running conflict which ran a lot longer.
The US was also coming straight out of WWII, so the idea that you should deal with belligerent countries pro-actively sounded like a really good idea and provided a great narrative, the communist threat would have also seemed less intractable since you didn't have to deal with Nuclear arms race.
You've also got media actually showing the home front what the battlefield actually looks like, that's a pretty profound change from previously where media pieces were basically clips from war movies.
Finally you had a completely different culture in the 60's that was largely based on a rejection of authority, do you think that was going to mix well with the military?
You don't need Soviet propaganda to explain the Vietnam peace movement, the known facts are explained by the known facts.