Information privacy is not a central theme in Starship Troopers, however we can infer a few things about the fictional society’s view on privacy. The society is relatively fascistic, and the only public information source shown is the single government- controlled news network; even the internet never appears directly in the story. From these things it seems likely that censorship is rampant in the society and things like mail privacy and search warrants do not exist, though since the characters never do anything the government wouldn’t want them to we can’t directly test this.
A direct piece of evidence for the society’s lower expectation of privacy compared to ours is the fact that students’ test scores are public: students can apparently only view their test scores in a single public area where all their peers can also see. It is unclear whether that is true only for high stakes test or for every grade the students receive, or whether that is unique to older students or occurs even in early education. It is worth noting that high school students’ test scores are public in some other democratic countries in the real world, like India; this example should not be given undue weight.
The shower scene is relatively lewd by modern standards, possibly indicating a lesser sense of physical privacy in the depicted society. On the other hand, it may have simply been a device to show off the actors’ physiques to the audience.