So it's interesting that you mention the Vietnam War. Hogan's Heroes was really one of a large number of shows, from Gomer Pyle, USMC to McHale's Navy to F Troop, in the second half of the 1960s which treated war/the military with some level of humor and/or satire. Similarly, there were a number of shows, from I Spy to The Man From UNCLE to Get Smart, which gave similar treatment to espionage. What this basically means is that the two major conflicts of this era- the Cold War and the Vietnam War- were both essentially being well covered by the TV sitcom landscape in this era. There is an interesting case to be made for Hogan's Heroes as a commentary on the Vietnam War at its most volatile peak, in the way that MASH (which came out only a year or two after Hogan's Heroes was canceled) was clearly, despite being set during the Korean War, a commentary on the Vietnam War in its waning days as the war's futility was crystal clear. (One of the creators of MASH, Gene Reynolds, actually directed 34 episodes of Hogan's Heroes.)

The more important part, though- Hogan's Heroes was not that weird a show in context, when you break it down into elements. After all, sixties TV could often get much much weirder. This was a decade in which a TV show about a talking horse aired for six seasons, a show about a flying nun aired for four seasons, there were two separate shows about families of supernatural beings living among "normal people," and a show about a family whose deceased mother was reincarnated as a car (called, of course, My Mother The Car) actually made it a full season. Not only was setting a comedy in a WWII POW camp not considered beyond the pale, Hogan's Heroes actually poached the idea from the creators of The Man From UNCLE, who had been planning a show at NBC set in an Italian POW camp, which they planned to call Campo 44. The show creators had originally had the idea for the show being set in a minimum security prison, but couldn't sell it until it had been rewritten for a POW camp. In many ways, Hogan's Heroes falls squarely into a show type that was almost typical in the late 60s: absurd situations, often with a satirical element, with funny and improbable gadgets, witty one-liners, and of course an everpresent laugh track. The fact that it was set in a war setting just made it part of a popular genre (and not even the only one set in WWII- McHale's Navy was set then as well). Indeed, Hogan's Heroes was quite popular, and was nominated three times in a row for Outstanding Comedy Series, and nominated a number of times for acting awards, with Werner Klemperer, who played Colonel Klink, winning twice as Oustanding Supporting Actor In A Comedy.

So then you end up with the elephant in the room- the fact that the war in Hogan's Heroes isn't the Civil War or the Korean War or even WWI, but WWII, and that it, unlike the prospective Campo 44, was set in a German POW camp, not an Italian one. This is absolutely not something that was lost on people from the very beginning; someone who was watching the pilot of Hogan's Heroes would notice that a main POW character, Vladimir Minsk, played by Leonid Kinskey, is gone for the rest of the show, replaced with Andrew Carter, played by Larry Hovis, who had actually played a one-off character in the pilot. This was because Kinskey, one of whose notable earlier roles was as Sasha the bartender in Casablanca (in which he was one of a large number of refugee actors reacting viscerally to the war), was a Jewish refugee from the Nazis himself who had a visceral reaction to the show when he arrived on set; he later said, “The moment we had a dress rehearsal and I saw German SS uniforms something very ugly rose in me. I visualized millions upon millions of bodies of innocent people murdered by the Nazis. One can hardly, in good taste, joke about it.”

(Incidentally, another thing that one would notice is that the pilot is a comedic rip-off of the plot of the film Stalag 17; while Stalag 17 was itself a comedy set in a WWII German POW camp, featuring its own proto-Sergeant Schulz down to the same name, the plotline that was being mocked in the Hogan's Heroes pilot was not comedic in the original movie. The rip-off was so blatant that the writers of the play on which Stalag 17 was based actually sued the show unsuccessfully.)

Interestingly, though, in fact every one of the main German soldiers on the show was played by a Jew (Werner Klemperer, John Banner, Howard Caine, and Leon Askin), and all of them but Howard Caine were played by refugees from the Germans (John Banner and Leon Askin left Austria after the Anschluss, Klemperer left Germany in 1935). This fact in and of itself was not unusual- a large percentage of Nazi roles in Hollywood in the decades following WWII were played by Jewish refugees (Klemperer had previously played a Nazi war criminal in Judgment at Nuremberg), but the fact that this was a comedy made it somewhat distinctive. One of the creators of the show (who were both Jewish as well) actually said that they consciously had Jews portraying Nazis as a way to mock the idea of Nazi supremacy. Robert Clary was a Jewish Holocaust survivor from France who spent much of the war in Buchenwald. And another point- you ask about the reaction of US WWII veteran viewers, but in fact these same refugees were also WWII vets- John Banner, Leon Askin, Howard Caine, and Werner Klemperer all served in the US Army, and while the actors playing POWs were too young to have served, Richard Dawson was evacuated as a child from the bombing in London. Klemperer himself, when asked about the show, made the point that it was a sitcom about human relationships that could have happened anywhere- "it could have happened in a factory of General Motors, for God's sake!"- and that while initially he'd been stunned to realize that this standard Nazi role he was screen testing for was actually meant to be comedic, he soon realized that it was a satire and played the role with the understanding that the Nazis could never win.

Now, a major element here that makes the fact that the show, unlike Campo 44, was set in a German POW camp rather than an Italian one is the fact that this show could be said to be furthering the "clean Wehrmacht" narrative. For much better discussions of this conceptually and factually than I could ever write, see u/commiespaceinvader's posts here and here. The main idea, though, is that while perhaps the erstwhile creators of Campo 44 could have written a show in which the POW camp administration is apathetic, incompetent, and even possibly sympathetic, as they were dealing with Italian soldiers, the same could not be done for German soldiers. While of course this is a very valid and I'd say justified argument to make, I would argue that the show's creators put at least some effort into minimizing it on the show. Klink and Schulz, the only German soldiers in every episode, are portrayed not only as bumbling buffoons who would rather not be at war at all (and in fact cherish their current placement as a vastly superior alternative to being sent to the Russian front), but are also portrayed as being under the thumb of General Burkhalter, Klink's commanding officer, and Major Hochstetter, of the Gestapo. While initially they are interchangeable (literally- if one of the actors wasn't available, they'd call the other one and change the name in the script), they later faced off against each other as representatives of the military vs paramilitary/police organizations of the Nazi government, and also are clearly shown to be actually malevolent, and, usually, competent (when not being foiled by the POWs). It seems clear that if Klink and Schulz were at all competent, they could be just as bad. The question is whether this goes far enough in counteracting this narrative and preventing Klink and Schulz from seeming too sympathetic; an argument can easily be made that it did not. They were such buffoons and targets of cartoon violence, on par with a Wile E Coyote or Three Stooges, that viewers often considered Klink and Schulz to be their favorite characters.

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