no, it was really just the clothes they individually felt comfortable in and decided to wear. They were mostly living or working in London which was then the fashion capital of under-30 culture. As a kid I can remember seeing Beatles posters on my older cousin's walls, then seeing people on the streets dressed the same. They had an influence on fashion, hair length, glasses.
Around this time you began seeing men with long hair, beards and round glasses - clones of Lennon.
John was in his White Period with Yoko. That was an artistic choice and philosophy of sorts. Perhaps subliminally John felt some spiritual evolution epitomized by dressing in white. It looks like a white linen suit which would have been cool on this summer day shoot.
Ringo's fashion sense grew over the years and he hung out with Peter Sellers and other celebrities. He was comfortably dressed.
Paul is in his casual chic.
George is in his 'modest working-class' jeans making his personal statement. Lennon had been there during the White Album but moved on.