“Back in the USSR” was just a parody of Chuck Berry and the Beach Boys. There really wasn’t any political message in that particular song. McCartney wrote it, not Lennon, and McCartney didn’t tend towards the political.
And, to complete the circle, here is a parody of the Beach Boys California Girls about
Russian girls.
Well, Ukraine girls really knock me out!
I dig their flat Slav cheeks.
And the Georgian chicks with the way they kiss
keep their guys blue-balled for weeks.
I've been all 'round the CIS
but I never thought I'd find
a hot kulak with skin like chalk
blowing Ivan's Russian mind.
I wish they all could be Yugoslavic,
I'd give my yurt for some Upper Baltic,
thank God you're no Mongolian girl!