SPECTRE included members of SMERSH in its war council or whatever the leading body was called. Using Soviets as full on direct enemies was avoided, I think, because it was too on the nose and would have raised controversies. I enjoy the way the Bond films, as well as films like Red October, show diplomatic relations between Soviets and the west. The cooperation is mostly BS, and I think doesn't reflect the real world at all, but those kinds of scenes make for nice food for thought about geo-politics.
Guys at the UN probably didn't want to hear the USSR quote From Russia With Love lines as evidence The Capitalist West's objections to aggression and gulags were actually bigotry toward egalitarianism. Of course, there's now some irony in that.