Thank you for the correction. Yes, I meant the unnamed character refusing to eat Green Eggs and Ham.
You are right that the overall moral of the story doesn't change, but the narrative does if you switch the color and food item entirely. For example, many kids don't like peas period, so they may actually side with the unnamed character's opinion on refusing to eat Peas altogether. Eggs and Ham are chosen because they are commonly known good-tasting foods that not many people have problems with. Peas and Lamb on the other hand are much more questionable. I know some people who absolutely hate the taste of Lamb.
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Why would it be a big strike? It's not like the Dwarves would suddenly be Blue just because Tolkien was never specific to assigning a particular skintone to the race.
If Frodo were reacting in shock to pink haired men from the south instead of them being dark skinned, I would say that the narrative is changed quite a bit. To the reader, it would be more confusing or amusing, depending on how seriously this is meant to be depicted. I'm not sure why you even use this as an example.Black Humans. And is that even that important to the narrative? If you swapped "Black Skin" with "Pink Hair"...wouldn't that make them just as notable?