There are estimated to be between 5000 and 8000 members in the KKK. It is at its lowest number of members and groups in history. And at least historically, it has not been Republican.
Republicans don’t claim the KKK, and the KKK doesn’t claim to be Republican. White separatist groups or neo-Nazi groups, perhaps another 10,000, are not welcome in either party. You don’t find any recognized faction within either party that is allowed to operate at their conventions. They are fringe, not allowed to participate, nor are their platforms in the various main party platforms.
The KKK was at one time very much part of the southern Democratic Party. The current membership has been denounced by every Christian denomination known, and has been rejected by both the Democratic and Republican parties.
The group is very fringe. However, the Nation of Islam, run by Farrakhan, is large and active politically in the Democratic party. It is probably 10 times larger than the KKK. And occasionally, you’ll find it and Black Live Matter have contingents in the Democratic contingency at ralleys and conventions.
Oh and STFU