The Communist doctrine requires that everyone work together, as a community, to the benefit of everyone. More specifically, there is generally a specific group advocating this lifestyle that insists everyone else joins for their own good.
The Brotherhood in its classic incarnation (see the differences between the Outcasts and the Lyons Doctrine) is entirely disinterested in the people of the Wasteland, and work to advance their own agenda - find and secure pre-war technology before it is lost forever. Even the Lyons branch of the Brotherhood see themselves as a security force, fighting to protect the locals from the Super Mutants without ever insisting they join up or contribute.
The Communists mentioned in Fallout 3 are the Chinese, who were at war with America up to 10/23/2077 when the bombs fell. Fallout 3 begins 200 years later, and the issue of Communist versus Capitalist has been largely abandoned in the face of the more pressing philosophical debate of See Another Sunrise versus Die a Horrible Death. Plenty of pre-war propaganda survives, however.
One such surviving pocket of nostalgia is a squad of Chinese Remnant forces who survived the War, became ghouls and set up a base in Arlington Cemetery, not far from the Citadel. Radio broadcasts can be picked up in the region that repeat Communist propaganda recordings. These can be heard near the Citadel, but the Brotherhood seems to prefer Galaxy News Radio. With the Super Mutants and Enclave to worry about, the Brotherhood of Steel couldn't care less about a war that everybody lost two hundred years ago.