Word of warning. I’m going to discourse both on the book and on the Verhoeven’s movie.
He didn't include them as "grunts" probably because the training was sufficiently hard that most wouldn't have made it. If you read the description of the training it wasn't just 12 weeks square-bashing, it reads far more like Special Forces.
It might also have been because he was paying lip service to a society kind of modelled on 50s America where the ladies were the home-makers and females in the frontline weren't even on the radar.
However, having said that, we have the fabulous line about females in high rank and esteem:
"If the Almighty ever needs a hand to run the universe: hot ship pilot Yvette Deladrier" after Starship commander Deladrier brakes her ship's orbit to recover a lander that has blasted off late and which otherwise would miss rendezvous and all on board would perish. I’ve heard from a lot of my friends saying the movie version is utter shit. I’m not so sure. The thing is, Verhoeven was a master of taking existing texts and subtly pushing them into satire by overdoing Hollywood/MTV filming tropes. The viewer was encouraged to look at the films as broad entertainment and then ask what the actions of the heroes had to do with American culture. He did the same with Joe Eszterhas's scripts for “Basic Instinct” and “Showgirls”. “Basic Instinct” is a detective story where the 'hero' is someone who's already gotten away with murder because of his badge, and who shoots another innocent victim before the film is out, while the 'villain' is never actually shown to kill anyone. She's chiefly a suspect because of her sexuality (which is why GLAAD picketed the film) and lack of shame about it. “Showgirls” meanwhile depicts a vision of Las Vegas as a patriarchal dystopia where every woman is judged on her body and literally every male character is a predator of some kind. The fact the film is framed as a “Star is Born” story is even better when you consider all the revelations going on in Hollywood right now. If anything, it's timelier than Starship Troopers.
The movie is the opposite of the book. The movie is not in earnest, the book is. It's probably a failure of Verhoeven's in that respect. “RoboCop” was seen as a satire from the get-go. I don't think there are enough sign-posts in “Starship Troopers” to stamp it as a satire outright, although it clearly is in hind-sight.
Verhoeven's early life was under the Nazis. When the movie came out Iwas on an internet forum and we were relentlessly trolled by a few young Americans who took it seriously as an action film, as some kind of heroism to emulate. It was actually a while before the film was released in the Portugal, so I didn't have much to say until I saw it. That's when the satire was obvious to me, but I also realised how teenagers would just go with the fascism (not even realising it was fascism) and feel it was a good thing. The problem was that, just as in “Robocop” (and “Showgirls”, to be honest), Verhoeven's satire comes within some superb plotting and film design that, if one is not careful, might actually seem sincere. Unbelievably, a lot of critics just didn't get it at the time, especially American film critics. I wonder if they didn't want to get it - far too close for comfort to an attitude among many in American society (and not just American society): a simplistic good versus evil narrative with the only solution being to crush the evil-doers with overwhelming force.
As to the accusation that Heinlein was a fascist, you need to remember that he wrote most of his works over fifty years ago, in a VERY different world from ours. I want to say, he was the first one to have a Japanese American Hero - Jeff Mitsui in "Sixth Column", the first to have a Hispanic hero - heck a bunch of them - in "Starship Troopers" - Juan and Simon Rico, Carmen Ibanez, David "Dizzy" Flores - all of them quite literally "white-washed" by that never-to-be-sufficiently-smartaleck Verhoeven in the movie. Col Dubois and "Ace" Smith were both black in the book, but "White-washed" in the movie. In "The Star Beast" - the true hero was the Assistant Secretary General of the United Nations, Samuel Kikui, a Masai tribesman from Kenya, with a Doctorate from Cambridge. In "Stranger in a Strange Land" - Judge Jubal Early spoke Arabic, "because he wanted to read the Quaran in the original Language of the Prophet." As I said, the book was written in the 1950's so must be read in the context of that time - not 'fiercely rightwing' at all. Robert Heinlein's attitudes changed as the times changed - communes and homosexual love featured in his books and not in a negative way. I feel the book and movie are far too divergent to reasonably discuss both as if they were the same. Each is its own standalone message and art. It's similar to the Japanese movie Kairo and its American remake “Pulse”. Even though both included a similar starting premise and “Pulse” even had some exact shot-for-shot scene recreations from the original, the stories diverge wildly and both show a very distinct difference between the cultures in how they tell stories and what they tell stories about. But "Heinlein is a conservative, white fascist" because that is a useful shibboleth for those who get their information from other people, who are too busy to actually read what they are condemning. Heinlein had a long fascination with the risks of universal enfranchisement. This is of a piece with American concerns about majoritarianism. In “Expanded Universe”, he goes through a few ways in which the right to vote might be restricted in aid of better governance and decision making. My favourite example is his suggestion that only women be allowed to vote, because men have made such a god awful mess of things for such a very long time. It's never clear how serious he's being, except insofar as he is concerned that democracies often make idiotic decisions (alluded to in “Stranger in a Strange Land”, also). And honestly, in this world of Trump and Brexit, he's got plenty of company, even if lots of us still hew to Churchill's dictum in the end. Because of a few "brain bugs" is considered a fascist? The mass insects were brainless ferocious foot-soldiers. Round these parts, of course they'd be considered misunderstood and victimised. The humans weren't great, but we can’t make the bugs to be the good guys, right? The future Earth depicted in “Starship Troopers” didn't have nationalities just a common Earth citizenship. Plus men and women of multiple races fighting and showering together. What could be more democratic? Epic comprehension malfunction on the part of some of the readers, so to speak.
Piece of advice. Don't watch the film - read the original book! It predates the film about 40 years and - shock, horror - in the book our hero Rico is of good, solid South-American stock (as is the school's math-wiz, Juanita, on which Rico has a mild crush). Worse, he doesn't get the girl. Nobody dares tell Donald, in case he would reach for his tweeter...
Heinlein speaking as Heinlein put his money where his mouth was - joining the navy and serving his country. As a volunteer; he memorably denounced conscription under any circumstances as slavery.