"You don't want the gay liberation movement to morph into something like the Ku Klux Klan, demonstrating in the streets against Catholicism," George said Wednesday.
The comment came after organizers with Chicago's annual gay pride parade agreed to a later start time when Our Lady of Mount Carmel Church leaders complained a newly proposed route would block access to the church for Sunday masses, the Chicago Tribune reported.
George defended his analogy by saying, "The rhetoric of the KKK and the rhetoric of some of the gay liberation people -- Who is the enemy? The Catholic Church."
On Thursday, Equally Blessed, a coalition of four Catholic churches that work for LGBT rights, called George's statements "crude" and "demagogic."
"Cardinal George's offensive comments are further evidence of just how insensitive and out of touch the hierarchy is, and why opposition to its views is necessary," the group said in a statement.
"Whether it was the best choice of analogy I don't know. Taken out of context the meaning can be misinterpreted," an archdiocesan spokeswoman said. "I would suggest people read the whole interview."