"support" is a little ambigious, it can be to actively support or passively support by doing nothing. It would be odd to actively support a gov't who attacked your family, however, I don't think it would be that rare cause unlike here, where poltics is not directly tied to jobs (in that to get a good job in a business without being a solid republican or democrat), my guess is that in the Soviet Union ambition, whatever your particular ambition was, meant going through the party.
I just read a good novel that takes place in 1980's Soviet Union about a Soviet art critic called The Dream Life of Sukhanov, by Olga Grushin, its her first novel, but it was a very enteraining story to read and fairly thoughtful.
LSD needs a book board where people recommend books.