That's the conventional wisdom, but it's not really the case.
As late as November, 1969, half of U.S. college students supported President Nixon's Vietnam war policies. It was the 36% approval rating of East Coast college students that dropped it that low. In the South, it was 60%, the Midwest 52% and the West 50%.
U.S. college students, especially those in the East, outpaced the general public in opposing Richard Nixon's policies on the Vietnam War.
news.gallup.com
What turned public opinion were the increasing number of parents whose sons were coming home in boxes or not at all, the absence of a compelling argument or strategy for the war that was killing them, and the exposure of the degree to which the Pentagon was willing to lie about how the war was going.
And it's really easy to overstate the 60s culture as being defining for the Baby Boom. Remember---that's a group of people born between 1946 and 1964. In 1969---the year of Woodstock---more than half of Baby Boomers were 13 or younger.