Going back to the OP’s assertion, there is a lot of confusion here about the “hippies” and various other groups in the 60s but the changes that many have mentioned can be traced to very different movements and social trends that eventually blended together towards the end of that decade.
The beatniks: The term “hippie” originally came from “hipster”, which was used to describe the beatniks in Greenwich Village and San Francisco. Although beatniks were in some ways a media creation – the term was coined by SF Chronicle columnist Herb Caen - nevertheless, this culture nurtured the early 60s folk music movement and artists such as Dylan and Baez.
The civil rights movement: This focused on eliminating racial discrimination against African Americans and restoring their right to vote in the South. Brown vs. Board of Education (1954) provided initiative for the bus boycotts, freedom rides, and sit-ins of the late 50s and early 60s. But nonviolent civil disobedience was viewed as the way to force change by gaining support and attention.
Student protests: A pivotal event was the formation of the SDS in 1960. The organization had its roots in the labor movement but the famous Port Huron Statement articulated a broader agenda that included an end to threat of nuclear war, racial discrimination, and economic inequality. When LBJ the escalated the war, it galvanized the organization and the draft became the rallying focal point for the organization’s growth and influence.
The feminist movement or “women’s liberation”: A key trigger for this was Betty Friedan’s book “The Feminine Mystique” in which she argued that the structure of society was responsible for creating a lack of satisfaction and meaning in the lives of most women.
Psychedelic drugs: In 1960 a Harvard profession of psychology by the name of Timothy Leary returned from a trip to Mexico after eating psilocybin mushrooms – an experience which altered the course of his life. It was at the “Human Be-In” in Golden Gate Park in 1967 where Leary urged the audience to "turn on, tune in, drop out". This mantra quickly became the media catchphrase for the hippy lifestyle and view of the world.
So while all of these trends or movements had distinct roots, as the 1960s hurtled towards the crescendo in 1968 all of them had become inextricably intertwined. White student protesters from the SDS had traveled south of 1964 during the “Mississippi Freedom Summer”. The Beatles and Stones, who had been influenced by the original Beat Generation and the folk singers, took LSD. (Beat poet Allen Ginsberg had also participated in Leary’s Harvard LSD research project). Bra burning women and anti-war protesters incorporated the civil disobedience methods of the civil rights movement, etc. Remember also, that this was a worldwide phenomenon – or at least in the developed world. There has been a lot written about 1968 in particular. Student protests in France almost brought down the government and marked a watershed shift to the left in French politics. And it was not coincidental that this period of great social unrest occurred when the largest demographic cohort in history were in their most formative years. But as these trends became divorced from their raison d’etre they eventually imploded. By the early 70s the social unrest was over. But many historians have suggested that the real revolutions occurred in the 1970s when the Baby Boomers brought the values and attitudes gained from their impressionable youth into the mainstream as they embarked on their careers and entered into marriage.
So what are the legacies from the 1960s? The SDS influenced a generation of political activists in the ways of participatory democracy – helping to remove politics from smoke filled backrooms and bring issues into the public debate to the point that media personalities and even bloggers can have a major impact on political direction. The feminist movement helped pave the way in the 1970s for women to attend college and enter the workforce in unprecedented numbers, forever changing the nature of family and gender dynamics. Our views of mental health and mental illness, and even what constitutes “reality” were profoundly influenced by the use of LSD and other “consciousness raising” drugs. Current attitudes about the structure of organizations, the environment, and organized religion can be traced to the counterculture views of “hippies” via the Beat poets as well as the Eastern influence of Leary and Ram Dass, etc, etc. Of course there are both positive and negative aspects to all of these changes and those can be debated endlessly. But the point is that the “hippies” must be viewed within the context of the confluence of changes that were sweeping across all dimensions of society at the time.