I think this is a little more formal than what others have been posting, but here it is anyway. It's somewhat an expansion of the comment I made earlier, with some more points and some textual support:
From a surface reading, it appears that women are a respected group in Starship Troopers. Rico repeatedly speaks of the intelligence of his friend Carmencita (27, among others), and he admires the prowess of the pilots that fly him into battle (9). However, when it comes down to it, there is little place for strength and honor among women in his world. In fact, Rico's attitude towards women is indicative of the systematic lack of respect that his society accords women.
Rico has two key close interactions with women of his own age in the book, both with Carmencita Ibanez. In the first, he is surprised when Carmencita tells him she wants to sign up for Federal service, since "little Carmen was so ornamental that you just never thought about her being useful" (26). It is hard to overstate how well this describes Rico's attitude toward women, whether they be his peers or his superiors. Though they may have key roles, Rico never considers them to have any kind of fundamentally important role in the workings of the universe. In fact, when Carmen gains some responsibility, Rico begins to respect her, but only insofar as she gains what he considers to be masculine qualities â€“ he finally sees her as an "officer and a fighting man â€“ as well as a very pretty girl" (139). In Rico's eyes, a warrior must be male, and if Carmen has these qualities, they must be separate from her femininity.
At first glance, the pilots in Starship Troopers seem to be a counter-example to this prejudice. Though every single soldier in the M.I. is male, the navy pilots are invariably female, and play a vital role in getting the soldiers to the ground safely. They are well-loved by the men whose lives are in their hands, and they hold absolute authority over their ship. But really, how respected are they? They are at most mid-ranking officers, who control their ship and perform a specific duty. In their capacity as troop transport drivers, they simply take the soldiers from one place to another, and never participate actively in the battle. As captains of navy warships, as mentioned in the book, they stand off at a distance and pound bug planets into oblivion. They are never present in the grit of the battlefield, and thus have no way to gain honor and respect in the eyes of the army men.
The one non-pilot female mentioned in the book, aside from Rico's mother, is actually smarter and more on top of things than her superior, and yet explicitly cut out of the chain of command. This is Miss Kendrick, the secretary to Rico's instructor Colonel Nielssen at the Officer academy. Colonel Nielssen admits that he signs "anything, if Miss Kendrick has initialed it," and yet if he were to die, she would "not do a blessed thingâ€¦because she is not in the line of command and has no authority" (150). By all rights, Miss Kendrick should be the one making commands, but she is a woman, and thus is not able to gain the respect she needs to make such decisions.
In fact, no woman in Starship troopers would be able to reach a seriously high level in the military. In order to become a general, and command the overall structure, a soldier has to work his way up through both the navy and the army. Conceivably, a woman could work her way up through the navy, but there is not a single woman in the army, so she could never gain the highest position.
Because of the number of women involved in the military, it seems that this power disparity would continue when the women returned from federal service. Rico's society is strictly militaristic, and the most respected roles are those of the military. It follows that the most respected individuals in the Federal government are those that participate at a high level in military service. In comparison to the size of the army, the navy is very small, in terms of man-power, and not all of the people in the navy are women. As such, the number of male respected citizens would far outweigh the number that are female, and so the women will likely have as little say in the non-military aspects of governance as they do in the military sphere.
This final effect of the societal disregard for women firmly marginalizes them in the Starship Troopers universe. They are respected in some small sense, but nevertheless are systematically left out of any important, guiding, decision-making capacity.