Popular Front culture was by and large subordinate to the Party. How many ex- (and not quite so ex-) commies later complained about how their articles, books and songs had to reflect the Party Line and the CP's view of Americanism? No, not every single person had to bow to Browder and Co., but for many it was an ideologically rigid time.
I don't think the New Left and the counterculture merged all that much. Yeah, Country Joe and the Dead played rallies, but wasn't it the Panther, SDS (and later Weather) critique that the counterculture was decadent and frivolous? By the late-60s and early 70s, much of the New Left had hardened into a dogmatic and at times violent culture, while the counterculture began receiving corporate bucks to entertain the new consumers advertisers coveted.
Even in the 80s, when I attended cultural events tied to anti-nuke or Central American issues, there was usually an earnestness that drowned out the fun that we were supposed to have. I'd find more spontaneous human expression and happiness at the block parties in Alphabet City and parts of Brooklyn than I'd see at events organized by white lefties, where people tried to give you leaflets while you danced.
DP