Utopia is a vision of a possible future with a bit of roadmap for getting there, although it is understood that one will never arrive at the perfected "No-Place." Star Trek is not utopia, however, unless you are positing the historically imminent viability of ships two miles long traveling at warp speed, transporters that can beam people on to these ships from any other place in the universe even while they are in warp, perfect gravity control, and little whirring hand-held helicopter fans that instantly diagnose and cure any ailment.
Most importantly, you need a box that violates the laws of thermodynamics by magically and instantaneously conjuring, out of literal thin air, any meal whatsoever, artfully arranged on its dish, perfectly prepared and steaming hot. On your oral command, the box can also produce any drink, use-object or tool or artwork or collectible one desires, off a perfect database of all goods ever devised, with no need of farmers, manual laborers, or even robots. Is this communism, or a parody of communism? Have I mentioned the universal translators that render idiomatic any concepts spoken by any previously unencountered alien species, or the development of complete immunity to the microbes and chemicals of other planets?
But we are talking about fiction, so let's suspend disbelief and take it for what it is, shall we? Star Trek is not utopia and never has been. It is allegory.
Star Trek is a space opera fantasy, set a mere 200-300 years from now, in which the United States military has morphed into a federation of all countries on Earth, and Earth now leads or is first among equals within a vast and expanding alliance of planets. The union's most important institution, a space navy known as Starfleet, brings the Open Door and liberal concepts of human rights and international law to the underdeveloped planets of the universe, in competition with the undemocratic and aggressive empires of the martial Klingons and the wiley-cunning Romulans. Accordingly the USS ships pack a lot of supernukes and directed energy weapons, and these do tend to be used.
Supposedly this enterprise follows a supreme rule that prevents them from fucking up less advanced civilizations, but I don't believe this has ever been mentioned except as a prelude to finding workarounds or justifying violations. It is true they don't have money and seem not to own property, other than their rich personal collections of stuff. This is thanks to the aforementioned god-magic-tech, and because they are a modern military in which every single individual's place in the hierarchy and precise role (and uniform) as a specialist has been assigned by a perfect meritocracy. Everyone can be tracked 24/7 by everyone else thanks to a surveillance and communications system they wear on their chests in the form of a distinctive badge that also specifies their rank. "Uhuru, where's Mr. Spock?" "He's on Deck 9." "Why isn't he answering?" "I believe he is masturbating, sir."
Surely no relation to an evolving ideal American self-image was ever intended?
While in 1967 the style of action was more centered on the command principle and thus more explicitly authoritarian, sexist, heroic, and muscular, by the nineties and beyond rainbow teams of races and alien species collaborated to overcome their cultural differences and maximize their harmony and competence so as to achieve the best outcomes in their peacekeeping missions, such as to mediate the conflicts of the newly Balkanized Wormhole Sector after the fall of the Cardassian empire and the arrival of the green little money-grubbing Ferengi with their big noses; Jesus did I really see that?
On Discovery, it's reached the point where no character other than the Real Science guy seems to have any credible function, especially not on the bridge. They sit in rooms where the lighting would be blinding, at least to the humans, and mash a lot of buttons in front of gargantuan screens, speaking their brief competent-sounding lines and their tediously long prayer-meditation monologues. Meanwhile a supercomputer actually runs the ship.
After their shifts, they retire to the enormous and ultrastylish luxury suites typical of the yeoman sailor's life. Again, they enjoy the instantaneous availability of every conceivable consumer good, none of which I have ever seen them disposing. They also enjoy tours within 4-D simulations of any place or time in the universe on their holodecks. This illustrates that the main form of consumption in the modern consumer society is the vicarious consumption of goods and experiences by the rich and smart characters we watch and identify with in our entertainments. On the holodeck these characters do roughly the same thing, so it adds a meta level.
As of the late 2010s, some people have taken to calling this a vision of communism.