That may even have been true, just a century ago. IIRC, the Klan reached something of a membership peak in the 1920s or there abouts, and membership was definitely not limited to residents of Southern States...
It was true. The Klan did not exist in 1861-65. It was a post war creation of a defeated nation.
In some places the Klan was more directed at Catholics and Jews. Of course people didn’t have to be in the Klan to be racist or anti-Black, but the 1920s Klan wasn’t just about White racism.