In James Clavell's semi-historical novel Shōgun, the Japanese nobility on several occasions use the phrase "garlic eaters" in a derogatory manner to refer to Koreans. Further comments are made to the effect that they find the dietary habits of the Koreans repulsive; Buntarō at one point remarks "They cook meat all the time [in Korea], boil it or roast it [...] Koreans're animals, like cannibals. The garlic stench even gets into your clothes and hair."
Korea and Japan had just finished fighting a war at that point in history, so Buntarō's comments, and anti-Korean sentiments in general, probably reflect that. Additionally, I can't assume Clavell didn't simply invent this slur for the novel. But it made me wonder what this fixation on this particular aspect of Korean cuisine indicates about Japanese cuisine at the time in general - when you think of traditional washoku, most of the dishes that come to mind are relatively mild in flavor, with soy sauce and dashi providing the bulk of the heavier flavors. Garlic, peppers, and flavorful spices are practically absent.
So, two questions: First, is the use of "garlic eater" in this derogatory sense historical in the first place, or an invention of Clavell's? Second, what kind of seasoning and spices did Japanese people in the 16th and 17th centuries apply to their cooking? Was there a significant difference between the dietary habits of nobles (who might be more inclined to adhere to social taboos about not eating red meat) and commoners in that regard?
First, I can say that Chinese, Koreans, and Japanese all come up with some creative derogatory slurs for each other. Koreans use the term "jok-bal-i" to refer to Japanese. Jok-bal is pork feet, and the traditional Japanese sandals, "geta", split the toes into two groups and make a clip-clop sound, like a pigs cloven hoof. So that the Japanese use the term "garlic eater" seems equally juvenile and/or offensive, depending on the context.
Looking through the texts I have at home, I couldn't find an answer, so I checked the library.
Out of Evil: New International Politics and Old Doctrines of War by Stephan Chan talks about North Korea and says on page 104:
Under the Shogunate, the Japanese devised belittling names for the Koreans, calling them 'garlic eaters' on account of their diet and their breath. There is a somewhat crude joke that one thing that unites the Chinese and Japanese, and that is their shared opinion on what an odd and primitive lot the Koreans are.
I couldn't find a source for this in the notes or bibliography.
Searching for keywords, I've found plenty of examples of the phrase being used:
Humour Across Frontiers Or Around the World in 80 Jokes by Richard D. Lewis p157
On one occasion the Republic of Korea were playing Japan and their players had been in the country for a few days' training prior to the match. Japanese and Koreans do not get on together particularly well (Japanese go so far as to call their neighbours "garlic-eaters") and the Korean officials had found endless grounds for complaint...
Was this the mysterious Korean navy they had heard about? The sailors hoped so. That would mean a fast end to this matter. They would quickly defeat these stupid garlic eaters and then their Japanese army would do the rest of the job. Korea would be theirs, with China next.
Eat Your Way Around the World by Jamie Aramini p37
Koreans are often called "garlic eaters" by the Japanese. (Koreans love garlic while most Japanese despise it.)
All these different examples, I can't find any primary sourcing for it. Out of Evil mentions the Shogunate and The Fox with the White Scarf is set over a time of 400 years and mentions a Korean-Japanese naval battle. They're also two different genres, so I would say that it's safe to say that Clavell did not invent the phrase - it shows up in a cookbook, a book on politics, a British comedian's memoirs, and a modern take on an old faerie tale. I would also say that the faerie tale and the Shogunate reference, combined with the historical mutual dislike/distrust between Japan and Korea, and other slurs which are known and can be traced back, that it probably goes back quite a ways.
The biggest problem for finding a more solid answer (primary sourcing) is that it's most likely going to be in Japanese, and it seems like a pretty esoteric topic that I think nailing it down more is going to be pretty tough.