How did containment in the cold war violate american values (specifically liberty)?

The Containment policies during the Cold War violated American values because it created a hysteria over communism in which many rights to a person's belief were violated by the government.

Many people were suspected of being communist spies and the land that is based on "freedom of beliefs" would try and find anyone who believed in the communist cause to try and prevent it from spreading.

Also, their foreign policy regarding the issue changed.  They went from trying to be neutral to having to support other countries (which we now still do) to prevent communism from occurring.