The biggest contraction of Civil Liberties during the Cold War took place during the "Red Scare" of the 1950s wherein Senator McCarthy led a search for communists in the United States.
The 1st Amendment of the Constitution permits the Free Assembly of Citizens, so McCarthy and the others, due to fear of the Soviet Communists were illegally interfering with Americans 1. right to be communists and 2. right to associate with communists.