“Part of the KKK’s stated mission included protecting southern culture from Catholics”
There have been three unconnected eras of the KKK.
The 1st Klan was a resistance movement against the 10 year Republican military occupation governments of Reconstruction. It basically ended along with Reconstruction in 1876. That Klan had no interest in anti-Catholicism.
The 2nd era was inspired by the world’s first major motion picture Birth Of A Nation in 1915. It was a combination political and fraternal movement. Popular in the north and west in addition to the south. It was anti-Catholic and along with the WCTU it was largely responsible for passing Prohibition. Corruption and a couple of headline crimes ended it in the late 1920s.
The 3rd era Klan coincided with opposition to the civil rights movement. It doesn’t seem to have any particular concern with Catholicism. The anti-Catholicism of the 2nd era Klan was tied in with opposition to the heavy immigration in the early 1900s.
1947 Democrat Klansman on the Supreme Court hands down anti-Catholic decision against parochial schools
https://en.m.wikipedia.org/wiki/Hugo_Black