Actually, it is fully outside of Protestant confessions, and has long been condemned by majority of the same.
Though most members of the KKK saw themselves as holding to American values and Christian morality, virtually every Christian denomination officially denounced the Ku Klux Klan.
As for Caughlin, well, he kept his collar but lost his show and his audience.
Coughlin did not lose his show due to anyone from within hierarchy the RCC having taken it away from him.
Comparing Protestants to the KKK is the same as playing the Nazi card.
Time to invoke Godwin’s Law and declare victory.