No, its exactly the opposite, the first incarnation of Trek actually did feature Kirk travelling to an alternative reality in which the Federation was fascist and it was a very, very different place, with constant and casual violence, might makes right is at the heart of the fascist idea and ideology, and in many respects the Klingons in the earlier Trek where pseudo or proto-fascists but they were some what rehabilitated with later shows, such as Next Generation, and just their popularity among fans, and became a warrior state rather than a fascist one.
Although I would say that the Federation is a traditional liberal "empire", its multi-cultural, post-capitalist, lawful and reasoning, it is a place in which outsiders are welcome, even if they can become a figure of fun like Spock was with the frequent "Spock bits" were they laughed at his lack of understanding (the aspect of "teaching" or reflecting on how to be a person in the show has been picked apart and should be obvious, it may explain its popularity with certain demographics who think a lot about those things too).
Now, people hate that idea, for different reasons, post-modernists hate it because it can seem like a singular unchallenged narrative, and some of the later themes, the resurgence in metaphysics and spirituality in the one featuring a space station or out post (I cant recall its title right now) are a little post-modernist if you ask me, actual fascists are bound to hate it because of its liberalism and its voguish, in Orwellian style, to project and attack in that fashion, marxists hate it because it does portray a post-capitalist order but they suspect there's still class or social struggles unacknowledged or unawares going on (which I think can say something about some marxists and even some other sorts of agitators inability to imagine a time when "the war is over" or a real "end game").