C.U.N.T. wants to eliminate the internet. They want to protect children from pornography, perverts, and the manual making of nuclear bombs.
Their motto is: "CITIZENS UNITED NEGATING TECHNOLOGY FOR LIFE AND PEOPLE'S SAFETY." "For life and people's safety" gives the additional acronym FLAPS. When this is added to the other acronym "C.U.N.T." it spells out "CUNT FLAPS". This is obviously some of Rockstar's famed Adult Humor.
Another thing is the email address of the group: "JT@citizensunitednegatingtechnology.org". This is seen on the teaser sight, and JT could be a reference the initials of Jack Thompson, an arch enemy of Rockstar Games, who is perfect to be the leader of a video game hating group.
The in-game group had a website made for it before the release of the game to serve as a teaser site. It can be found here.