I've tried myself a few time to get this topic covered, so I hope the best of luck to this thread.
That being said, I have no clue how to get this to come about. Something to note though is why the counterculture died. There are a few reasons. First, the causes that inspired the most outcry were won or at least enough to take the wind out of the sails; we pulled out of Vietnam, blacks had civil rights, etc, etc. After that, it petered out.
Two, the counterculture assimilated into the culture. They didn't go away; they became the liberators of the mainstream. That's why you can wear a t-shirt and jeans and don't have to walk outside wearing a nice suit. That's why you can have any hair style or facial hair you want. That's why you can swear in mixed company. That's why on TV, you don't have to have couples sleeping in two beds anymore. They unpuckered America's butt.
Three, there were crack downs on the counterculture. Groups were infiltrated, seeds of dissent were sewn (there was the fake Black Panther coloring book or whatever it was that the FBI made up to make them look like they wanted to kill white people), everyone was getting probed and an FBI file, and so on.
Four, there was the backlash against the counterculture once it went more militant. Flower Power and all it's peace and love are something mainstream America can stomach, but Black Panthers and the Nation of Islam and the Weather Underground and all that, whether militant through actuality or simply popular conception, were something that made mainstream white Americans very upset. I'm not saying that was predestined, though. The later 60s and early 70s birthed the militants and radicals because of the times and the environment. Peace and love were being questioned because the problems of America were still there and Vietnam was still there, and authority figures were pushing back against it with violence often times, and so more and more people started to replace flower power with "by any means necessary"; what those means were depending on the group ideology. A calmer times would not have lead to all that in the counterculture; at least not as the big force it became. There's probably more reasons, but I can't think of them off the top of my head.
To summarize, the way you get a less militant counterculture is to remove the Vietnam war from the equation, and a less militant, peace and love counterculture seems to me to be one that can survive longer and not burn itself out.
Alternatively, maybe you can just go completely the opposite direction of that, have the militancy still happen, ramp it up, go to the extreme in that direction, and push many of the hippies to a position of separation from society. I've been thinking this sort of thing over for a future TL, with the idea to have multiple successful communes with commune hippies becoming like the Amish.