Plyushch became a dissident by taking a public stance on political hot topics of the time. In 1968 he protested against the misconduct of the Galanskov–Ginzburg trial by sending a letter to Komsomolskaya Pravda, which was not published. When Soviet troops invaded Czechoslovakia in 1968, Plyushch jointly signed with 16 other Soviet dissident a declaration of solidarity with the democratic movement in Czechoslovakia. In the same year he joined the Initiative Group for the Defense of Human Rights in the USSR, which sent a letter to the UN Human Rights Commission asking it to investigate the violations by the USSR of the right to hold independent beliefs and to propagate them by legal means. Plyushch was one of the fifteen signatories to An Appeal to The UN Committee for Human Rights. Due to blowback from his political stances, he was dismissed from the Cybernetics Institute in 1968, and the KGB confiscated a number of his manuscripts and interrogated him several times.