There's a bunch of factors involved depending on where the POD is, too. Do the Allies have the bomb and decide not to use it? Are there no nukes? Does Russia split the atom first?
I think the nuke was uniquely horrific and traumatizing, at least to an extent - look at the effect it had on Japanese pop culture - but it's difficult to fully disentangle that particular trauma from the trauma of everything else that happened in the war, or simultaneously the trauma of having their empire forcibly stripped away by foreign adversaries.
While I'm not an expert, I definitely agree that the controversy over Hiroshima-Nagasaki took a long time to grow into its present status. I'd estimate (again, without any expertise) that two of the major factors were (1) the above-mentioned expression of nuclear trauma in Japanese pop culture works like Godzilla and Barefoot Gen, and those works over time finding an audience in the west, and (2) the specter of nuclear holocaust hanging over everyone's heads during the cold war, making American citizens really conscious of 'oh shit, these nuke things are frikkin terrifying, huh?'.
(Actually, the latter part (in the US, at least) is probably tied in a lot with the peace movement, the hippie movement, the rise of environmentalism... and a lot of that's also tied in with Vietnam and all the shady shit the US military was getting up to overseas throughout the cold war, so that's even more dependent on which way the butterflies fly.)
In a hypothetical timeline where nukes were never used on Japan, I'd guess that there would be less controversy in alt!2023 upon the same-day release of... IDK, Raggedy Ann and Eisenhower, but it'd probably still be a controversial topic in the ATL. The major unknown factors are how much Japanese society is still traumatized by losing the war and their empire, how and how much that gets expressed in their pop culture over the following years and decades, whether Japanese pop culture gets spread over to the west and finds an audience there like it did IOTL, and how the entire cold war plays out in this other universe.