advocacy of a classless society in which private ownership has been abolished and the means of production and subsistence belong to the community
This definition doesn't apply to the Star Trek universe, as we clearly know that Picard's brother (First Contact) owned a vineyard in France. Sisko's father (DS9) opened a Creole restaurant with hand cooked meals. People still had houses, and possessions, and the system still used a form of credit. What Star Trek actually represents is a post-scarcity society, where most basic needs are provided by replicators, and by not being primarily concerned about survival, greed is not such a motivating factor as it is in real life.
How did it get that way? Let's take a brief look at the history of that futuristic society:
2026-2053: World War III - 600 million dead, many governments destroyed. By that point, we can assume most people were more concerned with day-to-day survival in a somewhat nuclear wasteland.
2063: Zefram Cochrane converts a nuclear missile into the first warp capable, human made vessel, the Phoenix. Him going to warp speed attracts attention of a nearby Vulcan ship, who come down and introduce themselves.
2151: The experimental ship Enterprise NX-01 begins exploring space beyond the Solar system, after a century of rebuilding humanity, during which famine and war are eradicated. All under the watchful eye of Vulcans.
With the help of the technologically advanced Vulcans, humanity was able to wipe out disease and poverty in less than a century. The Vulcans were also instrumental in guiding the politics of the era, and if anything, helped the humans to develop a system of "participatory economics". More on that later.
It wasn't until 2161 that the actual United Federation of Planets was established, a coalition of the Humans, Vulcans, Andorians, and Tellerities.
The United Federation of Planets (abbreviated as UFP and commonly referred to as the Federation) was an interstellar federal republic, composed of planetary governments that agreed to exist semi-autonomously under a single central government based on the principles of universal liberty, rights, and equality, and to share their knowledge and resources in peaceful cooperation and space exploration.
Hhhm, I wonder why it wasn't called the United Commune of Planets? Because, simply enough, it didn't have the characteristics of a communist society.
The Federation has:
the form of a post-capitalist liberal democracy and constitutional republic.
The legislature of the Federation Council is located at the Presidio of San Francisco.
There is an executive branch headed by a Federation President, who keeps offices in the Palais de la Concorde in Paris.
There is a judiciary branch as well, the highest court of which is the Federation Supreme Court.
And enforcing it all, we have Starfleet:
The Federation's scientific, diplomatic and defensive/military arm is Starfleet, depicted as being headquartered at Fort Baker, just north of San Francisco across the Golden Gate Bridge.
Now, in "future" posts, I'll describe the true communists of the galaxy, but for the time being, I'll give you a hint:
After a fact finding opening, I'll hand the debate back over to vkey08, with the hopes of clarifying her position. For now, "Live long, and Prosper."