It was real enough! To put it in perspective, though, one also needs to bear in mind how stuffy, drab and conformist earlier decades had been.
Just in case people think I'm joking, I'd mention that when it first became fashionable (or at least acceptable within the peer group) for young men to wear long hair and sport what was in effect a 'unisex' hairstyle, many older people reacted with pure rage!
The 1960s had seen a whole series of 'liberal' reforms starting with the decriminalization of attempted suicide in 1960. Later changes saw the decriminalization of homosexual acts between consenting men aged 21+ (subject to a range of restrictions) and easier divorce ...
There were new kinds of popular music - the Beatles, the Rolling Stones and others.
In suburbia, moustaches started a-twitching and many older people succumbed to fits of the
shrieking ab-dabs ... Absolutely furious readers' letters appeared in some newspapers about how far women could enjoy sex ...
There was the mini-skirt, the sudden arrival of what were originally marketed as "kinky boots" - till the manufacturers discovered that the name was - even in the new "permissive" atmosphere of the time - so daring, not say shocking, that it was discouraging some women from buying them, and a new name was found for them.

(There were, after all, limits ...

)
Early in the 1960s the contraceptive pill became available, too.
There was a new hedonism, even shamelessness. Antonioni's film "Blow Up" (1966) encapsulated some of the brashness of it:
http://www.cinematheque.bc.ca/archives/blow.html
The late 1960s (c. 1967 onwards) also saw student protest on a hitherto unimaginable scale. Some of it was directed against U.S. involvement in Vietnam but also against petty-fogging regulations at the British universities.
(In those days it was still quite possible for a students to be expelled from university without any kind of formal proceedings, just on the say-so of the Vice-Chancellor, for such catch-all "offences" as "bringing the good name of the university into disrepute"). At the time, university students in Britain were a very, very small minority of their age-range - the figure rose from about 2% in 1960 to 8% in 1970 - and protests and demonstrations by what was regarded as a very privileged, small elite weren't well received by the public
Before continuing, however, there's an important point. It was above all the young who were the bearers (and consumers) of much of this.
In the 1960s I was first at school, then at university. Like many others, I was ambitious, and I found I had to work very hard indeed. I also felt I owed it to my parents to make a success of things and to keep out of real trouble.
As for politics and the new radicalism, I was never more than half convinced ...
Personally, I felt I was a spectator rather than an active participant in most of this.
______
PS. Many "traditionalists" view the 1960s with horror. See, for example, this link:
http://www.melaniephillips.com/articles/archives/000567.html