How to reconcile the evidence? I would suggest that it is only Earth that is socialistic, while the other member worlds have free market systems or mixed economies. The human-dominated Star Fleet military is the only Federation military force, and is tasked with collecting tribute from the nonhuman planets for redistribution to Earth. But as long as they pay their taxes, which subsidize Earth's welfare state and Star Fleet itself, they are largely left alone to govern their domestic affairs as they see fit. The Federation isessentially a big protection racket (in both senses of the word: providing external security, and also "protection" against its own depradations).
Why don't we ever see Captain Kirk or Capt. Picard on tribute collection runs? Because the Enterprise is one of Star Fleet's most advanced warships, and is therefore reserved for more difficult missions, such as going "where no man has gone before" in search of new wealthy star systems to occupy and tax.
If Gene Roddenberry were alive, I doubt he would be happy with this analysis. It makes the Federation seem somewhat less than ideal.