When you say "intertwined," do you mean in certain political aspirations (providing basic human services to the population, etc.), or do you mean that the "movements" were themselves politically aligned? If you mean the latter, I'd have to disagree with you. The Communist Party typically clashed with liberal parties during the twentieth century, beginning with the Bolshevik overthrow of the provisional government in 1917 and reaching a climax during the Cold War when the Communist Party liquidated liberal parties like the Democratic Party of Slovakia in order to achieve total power--not to mention that the Cold War was primarily waged between the liberal-democratic United States and the Communist-led Soviet Union. On this second point, keep in mind that the Cold War reached its peak during an era of liberal dominance of the Federal Government of the United States (1945-1968). In all here, I'm really asking for a clarification of what you mean by "intertwined" and when and where you see this interconnection.

Like @true_new_troll, I'm not sure what you mean by "intertwined"; I also am not clear on what you're including under the label "liberal." In addition to the conflicts that @t_n_t mentioned, there were quite a few organizations in the U.S., both before and during the Cold War, that could be classified as "liberal" under various definitions, that were strongly anti-Communist: the Socialist Party, the American Veterans Committee (not the current group with that name, but an earlier one that disbanded in 2008), and Americans for Democratic Action, among others.

TIL. Thank you /u/true_new_troll and /u/DudeTheObscure