When I was much younger and less knowledgeable about the world, I heard George Harrison's song "My Sweet Lord."
At first, I thought it was a Christian song due to the lyrics (including repeated use of "Hallelujah") and the fact the Beatles were English (Britain being a predominately Christian country, probably more so in the 1950s and 1960s than today).
Then he started singing "Hare Krishna" over and over again.
So here's an idea? What if, rather than dabbling in Eastern mysticism, Hinduism, etc., the Beatles were Christians?
This does not necessarily mean they'd be particularly weird Christians--you could associate them with the Jesus People movement if you want, but them being plain Anglicans would be fine. I would imagine this was the faith they were raised in, after all.
Obviously this George Harrison song would not exist and if John Lennon were a bit more continent, we would be spared Yoko Ono.
However, there are probably some greater socio-cultural effects. There might not be as much interest in Hare Krishna, for example, and that would mean less or no "deprogramming."
http://en.wikipedia.org/wiki/Hare_Krishna
http://en.wikipedia.org/wiki/Deprogramming