Regardless of speculation about the movies universe the point is the movie is a satire of facism, as that’s how the director interpreted the book (that is, fascist in nature). A lot of people missed this about the movie. If the arming of kids and sending them off to war, the slogans, the service guaranteeing citizenship and as I mentioned in another comment, the SS uniforms, don’t convince you. Maybe the directors own words will:

Although some contemporary critics and audiences considered Starship Troopers to be an endorsement of fascism, Verhoeven said, “whenever you see something that you think is fascist, you should know that the filmmakers agree with your opinion”

Edit: check out the wiki if you’d like to know more.