I suppose Korea congealed in a time before nationalism

Yup.

Before the Republic of Korea and the Democratic People's Republic of Korea, there was 35 years of Japanese colonialism. Before that there was 518 years of Joseon. That's longer 209 years longer than the United Kingdom has been around, and it was founded 315 years before the UK.

Before Joseon, there was Goryeo from 918-1392, 474 years, and before that, there was the Unified Silla from 668-935, and before that was the Three Kingdoms (Silla, Baekje, and Goguryeo) period from 57 BCE to 668.

If we say that the three kingdoms were different ethnic groups, then it would be easiest to say that 668 is the beginning of a mono-culture, when a unified Silla controlled all of present day South Korea and North Korea up to the Pyongyang-Wonsan area. However, Unified Silla experienced rebellion and infighting from the Baekje and Goguryeo, and they finally came under the control of the Goryeo, who were the descendants of the Goguryeo people, in 935. If that's the marker, then it's been 975 years of a mono-culture.

What happened to any groups that might object to the idea of One Korea?

As a state, there was no "Korea." It was "Silla" or "Baekje" or "Goguryeo." As for what would happen, it depends. Many of the defeated Baekje (people from the southwest of Korea) moved to Japan where they may have become the warrior/ruling class. This is disputed, especially given the history between Korea and Japan, but there is solid evidence that shows this is both possible and probable. Some of the groups decided to go to China and get support from the Chinese, namely Silla and Tang. This is particularly ironic when you read about some South Koreans complaining about Chinese intervention during the Korean War - anyone historically from the North would have been descended from Goryeo/Goguryeo, while many folks in the South would have been from Silla - the group that originally invited the Chinese in to help THEM.

Long story short though, "Korea" as we know it is a modern idea. The Three Kingdoms fought with each other for supremacy, finally unifying under Silla, who were them absorbed by Goryeo who became Joseon. Over that 1,278 years, the 3-4 groups became 1.

All that said, even today, there is still some division in Korea. Jeolla-do, the former Baekje region, is politically liberal, while Gyeongsang-do, the former Silla capital region, is politically conservative with many of the ROK leaders coming from Gyeongsang. Those leaders neglected the Jeolla region which has lagged behind socially and economically for all of the ROK history. So while Korea is a homogeneous society, it still has its cracks.