The film intentionally satirized the book.
The book isn't exactly fascist though. Verhoeven said he didn't read the book and does not plan to, so he is satirising somewhat superficially.
Heinlein did explore a lot of various political systems in his books, and I think Starship Troopers is focusing most on voter engagement - how people who vote should know something about what they vote on, and that is why only those who served (which includes military but also other "national service" like being a worker colonising planets or postman or whatever) get vote.
Is that fascist? I don't think so. Is it a good political system? I don't think so either but it is a good enough idea for a book.