I would not go so far as to associate all Republicans with the horrible Duke and King. National Republicans universally disassociated themselves from Duke, although Louisiana Republicans did embrace him. And while the National Republicans were quite happy to accommodate King’s bigotry for 16 years, he finally became too embarrassing even for the Trump Republicans and he just lost his primary.
There is an interesting contrast to a 1980 congressional race in which KKK leader Tom Metzger won a plurality victory in a Democratic primary for a Republican held congressional seat in the San Diego area by 318 votes. Democratic leaders from the county to the national level all denounced Metzger the day after the primary. The conservative Republican incumbent, Clair Burgener, won 86% of the vote, setting the record for the most votes ever won by any congressional candidate in history. Metzger is still alive today, spreading hate at every opportunity. In 2016, when Trump was running for president, he wrote, “I do not support Donald Trump, but I do support the CHAOS he brings in his wake.”