Very rational, very cynical, very head-in-the-clouds, very intelectual, not very emotional, not extrovert. Seems INTP to me.
Very rational & cynical? Huh?? This is the guy who wrote "All You Need Is Love," "Give Peace a Chance" & "Imagine"-- three of the all-time hippie peace anthems. You could argue he only did it as a posture to make money, but that doesn't align with how vocal he was in opposition to the Vietnam war (among other things), & the fact that he spent several years in the late 60s & 70s basically going out of his way to piss off the government, to the point where the Nixon administration tried to have him deported & the FBI accumulated several hundred pages worth of files on him. He basically broke up the Beatles at their zenith as a cash-making empire so he could lay in bed with Yoko Ono. He made a point of speaking his mind even in the Beatles' early days as squeaky-teen idols, & kept that pattern throughout his life.
To be cynical is to act practically at the expense of idealism out of the idea that self-interest always wins. "If you can't beat 'em, join em". Unless you're talking about the ancient Greek philosophical school (which was really a form of idealism centered on virtue & harmonious living), John Lennon was the exact opposite of a cynic.
Still, I think it's possible he was an INTP, but the emotion in most of his songs makes me think INFP or ENFP.
I think George may have been INFP also do to his mystical religious focus (remember he was the Beatle most affected by their trip into India & meeting with the Maharishi & all that, & he was one of the few 60s musicians who maintained an interest in Eastern meditation & stuff like that throughout his entire life). But, I can see ISFP also.
As for Paul & Ringo, I agree with ESFP though I can also see ESFJ for Ringo.