When it was first formed in 1865/1866, white Southern males were favorable to it, especially if they were Democrats. It was a way for them to form a collective in the wake of the Civil War and find the comraderie they'd experienced in the Confederate Army, while also serving as a way to re-enter politics (since most white males had been disenfranchised at that point), legally or not.

Northern men were mostly indifferent to the Klan, unless they were interested in politics. Northern Democrats may have publicly supported them, or not, but most were pushing for their Southern brethren to be reinstated as full citizens.

Republicans, Northern and Southern, were the most outspoken about the Klan's activities and they tried to suppress them wherever possible, even using Federal troops during Reconstruction to protect blacks and other Republicans. They were the ones who established a federal inquiry into Klan activities and ultimately prosecuted them under the Enforcement Acts in 1870 and 1871 and the Ku Klux Klan Act of 1871.

Which version of the Kaln? There were multiple "rebirths".