Believe it or not, this question has been asked and answered before: https://ww.reddit.com/r/AskHistorians/comments/1olmzs/how_did_people_in_the_ussr_feel_about_the_beatles/

There's a bit about the reaction in the US here: https://ww.reddit.com/r/AskHistorians/comments/2am4dr/was_there_ever_any_kickback_in_the_us_because_of/

It was hugely popular in the USSR. Although, "Yesterday" was definitely more popular. There was a lot more diffusion of Western culture into the USSR than you might think. People made bootlegged records using old X-Ray film, earning them the nickname "bones." Granted, the hammer could be brought down on anyone possessing and or replicating these things, but there was definitely an appetite for Western music.