People who think Starship Troopers is fascist have only watched the film (in which case it's better to say fascist overtones) and haven't picked up the novel. If you wanted to classify the novel as anything, "Spartan" or just "militaristic" would be a more apt description. Although "fascism" is a practically hollow description that mainly means "something I don't like and want to call evil" most definitions would agree that it's a system of governance that places the state above the citizen. However, the narrative in Starship Troopers is quite the opposite. One of the plot points is that humanity has realized that preserving even one human life is worth the sacrifice of all of humanity. The story even purports that this is something akin to a mathematical proof.
One could always try to suggest that it's actually such a fascist shit-show that the characters swallow this wholesale, but that runs headlong into so much of what's presented as fact in the novel, including that military service is entirely voluntary and well as the main character's father being a successful businessman (i.e. wealthy despite being a non-citizen) who only later joins the military (and serves under his son) after his home city is destroyed due to the war. The armed forces even try to wash out people who join but did so out of childish stupidity, but at the same time don't discriminate against anyone and will gladly find someone infirmed or otherwise incapable of typical service a role to serve.
Needless to say, the system of government presented in Starship Troopers isn't fascist. People who think it is have only seen the film, which wasn't even based on the novel and only used the title for marketing purposes due to certain similarities in the plot. The director, Paul Verhoeven, has also said that he never read the novel. The film (which I do enjoy for a variety of reasons) is its own separate beast.