Finally, a question geared towards the very specific things I study! Plenty of Americans did eat organ meat, but the groups that did were not the mainstreamed white, middle class groups. When the government made a push to eat organ meats during the first and second world war, they were primarily targeting normative groups that could always afford not to eat "offal," the undesirable parts of the hog, cow, chicken, or whatever animal you're eating. There's no date that Americans stopped eating offal, because wealthy Americans never really had to eat offal. By the late 19th century, however, offal consumption was relatively rare in normative white middle class communities, and it wasn't until the second world war that it picked back up and was made "respectable."

I first want to bring up the prominence of offal in certain regional cuisines. Soul Food (and to a lesser extent, southern food) makes fairly extensive use of offal, namely ham hocks, chitterlings (pig intestines), and chicken livers, namely because the African American communities who originated soul food lacked access to cuts of meat that were "high on the hog." The material conditions of slavery also had an impact on the creation of soul food, as enslaved persons would have access to rations that only included the most undesirable parts of meat. Offal consumption often, though not always originates from conditions of struggle, which, over time, can transform "offal" into a regional delicacy. In the US, the use of Offal in soul food helped further racialize the consumption of Offal and discourage its widespread consumption.

The need for offal consumption in most of the 19th and early 20th century United States was low. The time leading up to the first and second World Wars was a time of relative material plenty. Especially among immigrant communities, who might've typically lacked access to meat in the "old world," the United States had abundant, inexpensive meat available to even impoverished immigrant communities. Readily available access to meat helped differentiate the United States from other countries' food cultures, so any "americanized" cuisine that came out of the turn of the 20th century necessary emphasized meat consumption. And you didn't need to eat livers or kidneys, because eating offal was not materially necessary for most groups and by the turn of the 20th century, its continued role in souther and soul food wasn't *just* one of sheer necessity, though low income groups still relied more on offal consumption. Cultural significance also continued to encourage offal consumption in some groups, while actively discouraging it in others. Why eat worse cuts of meat when you can eat better ones? Readily available meat products were something of a novelty, especially for immigrant communities. There was no need, in the age of mass consumption and meat processing, to make use of every part of the animal, and those who could afford not to always managed to avoid it. Rich and middle class Americans weren't eating Offal meat because they didn't have to, and because they didn't want to be seen as similar to poor non white groups who did, and immigrant communities didn't eat offal because they wanted to be seen as wealthy.

During the second world war, however, the high rates of American meat consumption just weren't sustainable, so it became a part of the war effort to encourage people to eat less meat and to eat meat more creatively. By that point, since offal just wasn't eaten, it was seen as exotic, unhealthy, unpalatable, and distinctively not middle class, so the propaganda effort focused on making offal normal and disguising it like other respectable, middle class meats.

If you're interested in learning more, I suggest Hasia Diner's Hungering for America as a great source on immigrant and American foodways, "The Modern Offal Eaters" in Gastronomica (which talks about the echoes of Offal consumption today), Amy Bentley's Eating for Victory, and "Islands of Serenity" on the ordered meal (Meat+ two vegetables), Psyche Williams-Forson's Building Houses Out of Chicken Legs: Black Women, Food, and Power, Adrian Miller's Soul Food

If you want to learn about Offal more generally, the 2016 Oxford Symposium of Food and Cookery was about offal, and they publish a collection of all of the papers given.