I'm going to start this off with a clarification of terms. Referring to the 'hippy' movements of the Sixties is both misleading and confusing, because there was no one movement of hippies, and it's hard to tell if you're referring just to the women's rights movements, or the gay liberation, or the students, or the black movements. I don't put any blame on you for confusing terminology, it's popped up a few times here, and I'm never sure how to answer.

So assuming you're broadly talking about the Sixties counterculture, which was made up of all these groups, and more, I can address the question better. On the titular query, yes, the protests were effective. They were able to establish an early foundation for anti-war protest. While they might not have converted the majority of the American population, they were able to bring attention to the issues. As to the second which asks about the claims made that politicians and citizens already wanted an end to war and that the movements hindered that, I would say no, that is false.

The anti-war protesters were not new protesters - they were those who had participated in the early Civil Rights movement, students from the Berkeley '64 protests, and groups like SDS that had criticised the government and the usurping of the peoples political voice. It was no single protest group, but rather an amalgamation of many. The war acted as a standard for them to rally around, which made their voices more potent as more numbers gathered.

SNCC, the student group that had been a major presence in the Civil Rights Movement had a focus on the war in 1965. Teach-ins at universities were attended by thousands of students. SDS held a protest in Washington D.C. in April 1965, with around 25,000 people present. This opposition to the war was covered by media, disseminating the views of the students to the wider public.

Senator Fulbright, launched "Congressional hearings to investigate US policy in Vietnam and publicly questioned Johnson's key advisers", but he didn't do so until 1966, two years after he helped pass the Gulf of Tonkin resolution, which gave LBJ wide power to increase the scope of the war. Martin Luther King and Bobby Kennedy didn't come out publicly against the war until 1967. At the start of 1965, there was broad support for the war among Americans, as long as it wasn't escalated. The advisors to the President knew about the anti-war sentiments that were present in 1965, but they were a minority view.

The high point of the protests arguably was 1968, when antiwar protesters disrupted the Democratic National Convention in Chicago. There were other high profile events too, such as Kent State in 1970. Both of these were more than 3 years after the first major antiwar protest in Washinton D.C.

It was the growing escalation of the war, and the much publicised protests of the early anti-war groups that led to wider questioning of the administration, and from there, to a much wider anti-war sentiment among both the American public, and the political elite.

Sources:

Eric Foner, The Story of American Freedom.

The following three are journal articles available at Jstor if you have an account, or access through a university or library.

Frederik Lovegall, 'Lyndon Johnson and Vietnam', in Presidential Studies Quarterly.

Mitchell K. Hall, 'The Vietnam Era Antiwar Movement', in OAH Magazine of History.

Sandra Scanlon, ''That Bitch of a War': Lyndon B. Johnson and Vietnam', in History Ireland.

I'll piggyback onto the (excellent) answers here by noting that a common saying among historians of the war is that the only thing more hated than the Vietnam War was the anti-Vietnam War movement. It was entirely possible to think that the war was a total waste and that it should end, while at the same time not feeling too warm about the protesters, due to their tactics, appearance, or whatever else. Plenty of veterans came back opposed to the war, but did not care to work with the antiwar movement. Usually that was because vets saw the movement as comprised mostly of naive kids who had avoided the war through college deferments and couldn't understand what Vietnam was really like.

u/The_Alaskan noted that the rising antiwar movement played a major role in convincing LBJ to not seek re-election in 1968. This was one of two instances where the movement played a direct role in influencing policy. The other came in late 1969, when Nixon canceled a planned bombing raid known as Operation Duck Hook in response to a huge series of antiwar protests. Nixon found it relatively easy to ignore the movement so long as it appeared to be a bunch of shiftless "bums" (Nixon's words), but the 1969 protests featured a great many people who seemed to be normal, hard working, middle class voters. That scared Nixon enough that he shelved Duck Hook.

There is also some evidence to indicate that the antiwar movement played a role in ramping up Nixon's paranoia to the point where he created the "Plumbers" outfit that later broke into the DNC headquarters at the Watergate hotel. Nixon hated leaks, and when the Pentagon Papers leaked in 1971 due to the efforts of the extremely antiwar Daniel Ellsberg, Nixon was furious. The Plumbers were an effort to end any future such leaks, but they wound up contributing to Nixon's downfall.

Finally, the movement almost certainly had an effect on individual policymakers, and thereby helped bring the war to an end a bit sooner than it otherwise might have. Secretary of Defense Robert McNamara, for instance, went from a supporter of escalating the war in 1964-65 to a deeply troubled man who supported withdrawal in 1968. This transformation likely would not have happened so quickly were it not for his wife and three children developing serious doubts about the war. McNamara's wife Marg developed an ulcer in 1967 that lasted until she died in 1981; her husband attributed that ailment to stress brought on by the war. McNamara's son Craig took part in huge antiwar protests while in college at Stanford, which drove father and son apart for some time. And McNamara was not alone in this regard - many of LBJ's advisors had to deal with tremendous turmoil in their personal lives due to family members who turned against the war.

Sources:

Small, Melvin. Antiwarriors: The Vietnam War and the Battle for America's Hearts and Minds. Rowman and Littlefield, 2002.

Wells, Tom. The War Within: America's Battle Over Vietnam. University of California Press, 1994.