First of all, I want to thank all of you for providing a ton of ideas.
While I've known about some of the hippie equivalents or copycats from outside the US, some of those listed in the thread are new to me.
The hippie movement had substantial Indian Buddhist and Hindu influences. If we could replace this with Sufi Islamic influence, we would get a very different *hippie movement.
Interesting observation. Obviously, there should be some sort of popularisation of Sufism in the developed countries in the ATL. Or maybe even archaic Middle Eastern religions, such as Iranian Zoroastrianism, could hook some people interested in a period "exocitism" fad and non-Euro-American spirituality ?
You're right on all counts. However, the rebellious generation would most likely ignore all of the strict aspects of Islam and focus upon the mystical aspects of Sufism.
Possible. A kind of watered-down, mass appeal accessible "MacIslam" that focuses only on the Sufi philosophy that developed fans.
I know next-to-nothing about Sufi, but from what I know about Islam in general(and assuming Sufi encapsulates some of the same tendencies), its countercultural followers would probably have to adhere to some more well-defined codes of behaviour, than what was permitted under Hinduism And Buddhism Filtered Down Through Various Individual Teachers.
On that score, I have an inkling that strict monotheism, by its very nature, would be a major turn-off for rebellious middle-class youth in the 50s and 60s. "Prophet Freaks" might end up somewhat like their namesakes in the "Jesus Freak" movement, some influence within the Religious circle of the Venn Diagram, but very limited influence in the Countercultrual circle.
The different nature of the religion would make a lot of the nuanses of the cultural fallout quite different, indeed.
Though it would be interesting to see how an Islam-influenced countercultre reacts to the emergence of the middle-east as a major focal point for US foreign policy in the 1970s.
Yeah. Hopefully it wouldn't lead to too much divisions and disagreements in society.
The Company Of Young Canadians was a rather lame attempt to co-opt the student-radical movement. Essentially by giving them government funding, while at the same time telling them that they could be independent of government direction.
Obviously, this group didn't catch fire with Canada's youth. There is a funny NFB film of Saul Alinsky on a trip to Canada, arguing with some CYC members about their goals, and telling them that no one in the rest of society wants to live like hippies.
Fascinating bit of history, even if this wasn't a spontaneous counterculture.
The same goes for Germany with its Halbstarken (juvenile delinquents), Gammler (dropouts) and then Blumenkinder (hippies).
Aside of the Blumenkinder, I haven't heard of the rest, so I might research them.
Of the Dutch groups, I've read about most of them.
One of my favorites was the Situationist International (SI).
The SI was an international organization of social revolutionaries, the exclusive membership of which was made up of avant-garde artists, intellectuals, and political theorists, active from its formation in 1957 to its dissolution in 1972. The intellectual foundations of the Situationist International were derived primarily from anti-authoritarian Marxism and the avant-garde art movements of the early 20th century, particularly Dada and Surrealism.
These are interesting due to the artistic connections they had. In fact, given some cultural elements of my timeline's 20th century, some equivalents of this group could make a lot of sense within said TL.
Another possibility is the Swing Youth/Swing kids in Nazi Germany, though they more resembled the Mods rather than the hippies. Like the Mods, they were obsessed with modern black American music and sharp dressing styles. And they even had a bona fide generational, cultural and political conflict with the Nazi authorities.
That's pretty hilarious.

And yeah, I can imagine the clash with the authorities, given the nazis' famous obsession with poo-pooing on most American cultural imports, or blaming jazz and swing for being "Jewish inventions", and other nonsense.
The European jazz/swing fans of the 1920s were probably more shocking to their parents than the Wandervögel. If you look at conservative opinions on jazz at that time, the general view was that it was dangerous jungle music corrupting European kids - it was probably more provoking than punk, gangsta rap and acid house put together.
This I know about quite a lot. The cultural changes after WWI in Europe alone were massive, even in staunchly, stereotypically old-fashioned and quaint countries like the UK, etc. The jazz and swing scene was pretty lively throughout Europe during the 1930s. Heck, even Slovakia had its
middle-aged proto-pop singers back in the 1930s:
https://www.youtube.com/watch?v=tm1PQoUFtS4 https://www.youtube.com/watch?v=RcI_BP836zA 
The generations that came of age in the late 19th century or early 20th century would've been irritated with "all this new-fangled, loud and brash nonsense".
In my timeline, the equivalent of pop is called
snap, and instead of evolving hand-in-hand with rock and roll, it first developed as a further mutation of swing and big band music with dancing by couples, and then into a kind of dance music that slowly got more intertwined with rough rock music analogue.