While music played a big part of social conversion aided by drugs, the driving force for most people was the war and they were fervent about the issue.
The demonstrations and anti-war sentiment grew during Johnson's presidency and the media was easy on him. Then he announced he would not run and Nixon won in '68 after the Bill Ayers inspired riots at the democrat convention.
For a brief time the democrat party was in the crapper. But the war sentiment turned people against the government and Nixon was the government. Since Nixon was a republican, the effort to turn the government around was pushed through democrat voter effort. Had Johnson continued as President, things may have been mush different.
The real catalyst was the shootings at Kent State followed by the CSNY song "Ohio" - 'Tin soldiers and Nixon coming'. The aftermath was the vast majority of the youth becoming democrats, but ironically the mantra most often heard was "government out of our lives". After decades of "question authority" being the underpinning of the free life style social change it is very ironic that the people still hanging on to that philosophy now look to government to run every part of their lives.