You must first understand different life was pre-Beatles/Dylan etc. In general, there were 2 things before the Beatles, mods and rockers, then came along the Beatles who started of with a mod image, and then transformed into the hippy image which gave birth to many alternative lifestyles which previously were looked down upon by society. We're talking about the most radically changing decade in recent history, in which the Beatles played a big part of, they weren't the only ones at the time, but they were certainly the most prominent. There's a huge jump between the transitions of what was acceptable and what wasn't between the 1950's and 1960's, values were questioned such as state religion and racism that hadn't been questioned for centuries, there was a huge relaxation of social etiquette.
The Beatles were the biggest band of the decade and the band that was always ahead of their times, say the Beatles had a new angle on one album, somebody like the kinks or the who, or the beach boys would be the next to follow them, most obvious comparison I can give you is between The Who's album "The who sell out" released in 1967, being much alike "Rubber soul"(1965) and "Revolver"(1966).
"Tommorrow Never Knows 1966" - A song about acid trips, "lay down all thoughts, surrender to the void, it is shining, it is shining" the void being a concept described by Timothy Leary a popular book writer about the drug, hallucinogenics weren't exactly acceptable then.
"Why dont we do it in the Road?" - a quite obvious taboo broken, this promoting their free love message
"I'm so tired" - Swearing in popular music was never done and remain acceptable before, "git" being much more taboo than it is today, since "bloody" was considered a swear word over here.
"The ballad of John and Yoko" a deliberate attack on the press and their coverage of John Lennon and Yoko Ono's relationship, also a clever reference to his "we're bigger than Jesus message" that he'd offended half the world with.
"Within You, Without You" - A introduction to a Hindu and Buddhist ideals, something that was quite alien to the western world at the time, also a powerful message within the song, and done in an indian classical music style.
"Taxman" - A direct attack at the state.
"A day in the Life" - a cynical tale of day to day life, which got banned in England for the line "went upstairs and had a smoke, and somebody spoke and I fell into a dream" rediculous I know, but it was apparently suggesting drug use.
"All you need is love" - Seen as an anthem for the free love movement that was a phenomenal change in culture.
There's many more
If you're looking for people influenced by the Beatles, the list is endless, many many musicians over the years will proclaim their respect of the Beatles, this is why many bands consider Abbey Road, the holy grail of recording studios. There's an endless list of people covering the Beatles, people cover them today, and it is still considered that nobody can ever successfully cover the Beatles.
just take a gander if your interested:
http://en.wikipedia.org/wiki/The_Beatles'_influence_on_popular_culture