No hint of Sexism? Women were officers only, and the big bad troopers had to stay in their own zone in the ship away from them
I'm a woman and have read (and enjoyed) Starship Troopers. And given its historical context, the book never came across as sexist to me. In fact, it's the opposite of sexism. Keep in mind the book was published in 1959, not long after women went from Rosie the Riveter to being depicted as so technically incompetent they were unable to even back up a car in many TV sitcoms.
When I read Starship Troopers, I was amazed at how progressive Heinlein was at making women the pilots of the ships, even establishing that they were better pilots than men. That was amazingly progressive for 1959! And the fact that women were given full status in the military (women were kept separate in the US Air Force, as WAFs, until 1976) and allowed to go into combat zones (USAF women were not allowed into fighter pilot training until 1993) was amazing!
Heinlein treated the women soldiers in this book as intelligent, capable, and competent in an era where popular entertainment often depicted women (those same women who had worked in factories and flew military planes as WASPs during WWII) as scatter-brained nitwits who must be patiently guided by their husbands. Starship Troopers is a feminist paradise compared to other works of that era.