Well, the hippies called themselves hippies and their anthems were sung by people like Bob Dylan. They saw themselves as a movement and it definitely involved politics. That’s different from other generations like the teenagers of the 50’s who were full of life and spirit and also has a lot of fun, but it was generally much cleaner. The 50’s teenagers didn’t care much about politics or movements.
The Beatnik thing began in the 50’s but that was underground and I think a lot of older people and some fairly perverse people.
Bob Dylan? The only politics in Bob Dylan (aside from the civil rights movement) was the politics of obscurity. He knew how to craft a line that you could interpret pretty much any way you wanted to interpret it.
The political labels came from older people and a lot of it had to do with the Vietnam War. The kids were so "political" that we were able to draft millions of them and have hundreds of thousands of them fighting in a faraway jungle all at once. If you think they were political, just try doing that today. ;-)