Anonymous, a loose coalition of hackers said the data was "a form of resistance" against racial violence.
A list of alleged KKK members published earlier in the week appears to have been bogus.
The list appears to detail social media profiles of people who had joined or "liked" KKK-related groups on Facebook and Google+. Many of the profiles featured racist imagery and slogans.
Anonymous said it had used human intelligence - not hacking - to create the list.
"This means that individuals on this list were often identified by human sources of information through both overt (interviewing expert sources) and covert (digital espionage/social engineering) methods," a statement accompanying the list read.
A separate list posted online earlier this week incorrectly outed several US politicians as KKK members and was quickly followed by a official Anonymous denial from its @Operation_KKK Twitter account: "The anons at the helm of this initiative vouch ONLY for the dox list that will be released from this Twitter account on November 5 2015", it said.
5 November is a significant date for members of Anonymous because it is the day that Guy Fawkes attempted to blow up the English Parliament in 1605. Guy Fawkes masks, made popular in the movie V for Vendetta, have become a symbol for the group.
The group launched its latest campaign, dubbed Hoods Off, after the Ku Klux Klan threatened violence against protesters in Ferguson, Missouri. People, including Anonymous members, took to the streets after a jury decided not to prosecute a white police officer who had shot a black teenager in August 2014.
`Never forgot`
In November last year, Anonymous launched denial-of-service attacks to take down a website associated with the KKK and also took over two Twitter accounts connected to the group.
"We never forgot your threats to the protesters in Ferguson, and we certainly never forgave you. And the same will be done to the threats you give now," it said in an online posting.
Anonymous expert Gabriella Coleman has described the outing of KKK members as a "comeback" for the hacker group, which has faced criticism for failing to control members and leaking inaccurate information.
The fact that fake data was leaked earlier will be seen as an embarrassment for the group that has become well-known for backing social justice causes.
In 2012 it exposed the names and personal details of people allegedly involved in covering up the rape of a 16-year-old girl in Ohio.
And earlier this summer the group took down the Royal Canadian Mounted Police website after one of its officers shot and killed a protester wearing a Guy Fawkes mask.
To coincide with Guy Fawkes night, Anonymous is also holding protests in cities around the world, including one in London where there have been at least 28 arrests.
