As noted in the question, Heinlein's writing career was long and started a very long time ago (1939-1987). This is a man who was born in the Bible Belt in 1907 and spent the first half of his life vigorously interrogating his own upbringing and coming to radically different conclusions about ethics and religion than the conventional wisdom of his native time and place. He had a considerable stylistic range and wrote on many different themes for some very different audiences.
As background, Heinlein was a socialist in the 30's, while later in life he tended to express libertarian views. His wife Ginny was a biochemist and a navy (WAVES) veteran. There is a story that when he was used on TV as a color commentator during the Apollo program, he flustered Walter Conkite by suggesting that women should be allowed to be astronauts. However, his views with respect to feminism and women's roles were certainly not PC by modern standards.
A big chunk of his early writing was his juvenile novels (1947-1958), many of which were serialized in the Boy Scouts magazine Boy's Life before being published as books. These are written for a nominal audience of teenage boys (although Heinlein prided himself on not talking down to his audience, and fought a running battle with his prudish editor over their contents). In some of these, girls and women are simply absent. One (Podkayne of Mars) has a female lead who is somewhat saintly and has a younger brother who [spoiler]
smuggles drugs and get hold of a nuclear weapon.
In several of the juveniles, there is the theme of the boy protagonist who is forthright and courageous but not terribly bright, and has to be helped by a more intelligent and sophisticated girl (The Star Beast, Has Space Suit--Will Travel). In Starship Troopers (originally submitted to his publishers as a juvenile), the protagonist ends up as a grunt in the interstellar marines because he isn't as good at math and electronics as his high school friends, but one of the women his age becomes a starship pilot. In one of the juveniles there is a surprise revelation [spoiler]
that a boy is actually a girl.
One of the juvenile novels (The Rolling Stones) features a cantankerous, hypercompetent grandmother who is an experienced spaceship pilot. In Starman Jones the teenage female lead hides her intelligence until it is revealed later, and in The Star Beast she sexually manipulates an older man (or tries to?) to humorous effect.
In Heinlein's books for mature audiences from before 1970, we see some of the same shticks, such as the confused or less intelligent man paired with the more experienced and intelligent woman (Glory Road, For Us The Living), and the hypercompetent woman (Glory Road, Farnham's Freehold). In Stranger in a Strange Land, the protagonist manipulates his own sexual biology to give himself an androgynous body.
Later in life, Heinlein ran into a series of health challenges that he feared had clouded his thinking, and he began to doubt his own ability as a writer. Around this time, he stopped accepting requests for revisions from editors, and started getting feedback mainly from his wife, Ginny. My judgment is that his writing from this period is almost all awful, but others disagree. One of the standard critical complaints about his novels from this period is that the characters are one-dimensional and not believable, and I think this applied to both his men and his women. Cases in point are the sexy madonnas of I Will Fear No Evil and Time Enough for Love. Even more cringeworthy is Deety in The Number of the Beast, who spends a lot of time thinking about how happy she is that her husband likes her big breasts. Friday, one of his stronger works from this period, has a female protagonist who is an artificial person and disbelieves her own self-worth, although the narratives show her to be a superior person in various ways. To Sail Beyond the Sunset features a female POV who is filled in from her sexy madonna depiction in earlier books.