In Legend, the Republic believes it will win the war against the Colonies if it can remove people with "bad genes" from its population. Its methods are extreme, but the Republic's relationship with eugenics isn't so different from events that have happened throughout history.
In the early 20th century, people began to accept Charles Darwin's theory of natural selection. Around the same time, scientists were beginning to better understand how traits are passed from one generation to the next. Many scientists felt that it would benefit society if they could prevent births of people with undesirable traits and thus breed them out of the population. The theory behind this view was that, since this would occur as evolution progressed anyway, governments that practiced eugenics were just speeding things up. Many governments held eugenics conferences and funded eugenics research. Most Western countries at this time participated in eugenics to a greater or lesser extent. It was very common for people with certain diseases - especially mental illness - to be forcibly sterilized. In America, eugenics was popular among social progressives who advocated for better conditions for the poor and the ill. Many believed that reducing the population of people with bad genes would eventually eradicate poverty and disease.
Perhaps the most famous examples of eugenics are the policies of Nazi Germany during the rule of Adolf Hitler. The Nazis implemented many policies that were common in America and other Western countries at the time, like sterilizing the mentally ill. However, they extended these policies to murdering people with many different kinds of diseases. They also used eugenics theory to justify the genocide of Jews, Roma, homosexuals, and other minorities.
After World War II, the Nazi Party's close association with eugenics led to its disavowal by most of its supporters. Although forced sterilization continued for decades in some countries after 1945, most proponents of this practice and of similar procedures distanced themselves from eugenics philosophy.