Fun fact about A Boy and His Dog: it's one of the primary influences (actually probably THE primary influence) of the Fallout games and their setting. In that sense, much of it is a criticism of Cold War American culture. All of the horrible stuff done to women in that movie is not an endorsement of it, but more of a direct criticism of the underlying misogyny in American culture. Also, it's based on a Harlan Ellison novella. Or collection of them, rather.
Article is a bit click-baity. Many of the survivors who saw the film were okay with its depiction and understood why the film presented the atomic bombings the way that it did. The film is ultimately about J. Robert Oppenheimer, and showing the physical outcome of the bombings would have itself been a potentially crass and shocking inclusion in a relatively subdued character study of a complex and tortured individual. Everyone knows that the physical outcome of the bombings on Hiroshima are shocking and terrible and left a lasting scar on the nation, coming to define the national identity of the Japanese, and especially Hiroshima natives that survived the blast, throughout the 20th century and into the 21st. But it's sort of like The Wind Rises. Oppenheimer was a physicist, and a very talented one. That his work contributed to the horrors of war is part of the tragedy of the individual and their story, just like it was for Jiro Horikoshi, the designer of the Zero.
Or as I like to call it, "Hobbitcore."