Yes - good point - a huge mistake on his part. Seems he tried his best to exclude himself from that group for decades thereafter ('52 onward). Youngins today will be shocked - shocked I tell you - to know how incredibly, openly racist many in the US were, well into the early 1980s, especially in the south and midwest. Even the honkies who had the one black friend would refer to him or her as one of the good ones, while discussing spear-chuckers and jigaboo's in the next sentence. It was distressing to hear that, while also "Christian" groups were throwing rocks at kids on school buses during the forced busing years of the early-mid 1970s, not wanting the inner city blacks in their white neighborhoods, or their kids in inner city schools. So in some parts of the US in most of the 20th century, the KKK was not properly understood, nor was its history. Robert Byrd actually helped pass the groundbreaking Civil Rights act:

Despite his early career in the KKK, Byrd was linked to such senators as John C. Stennis, J. William Fulbright and George Smathers, who based their segregationist positions on their view of states' rights in contrast to senators like James Eastland, who held a reputation as a committed racist.

During his campaign for the United States House of Representatives in 1952, he announced that, "after about a year, I became disinterested, quit paying my dues, and dropped my membership in the organization", and that during the nine years that have followed, he had never been interested in the Klan. He said he had joined the Klan because he felt it offered excitement and was anti-communist, but also suggested his participation there "reflected the fears and prejudices" of the time. Byrd later called joining the KKK "the greatest mistake I ever made."