The usual pretty crude pneumatic sex-fantasies cropped up... But women actually have a pretty dominant role in Heinlein's lunar society... It's a penal colony, and Heinlein reckons that means there are going to be far fewer women than men there - so he's come up with a system called 'line-marriage'... wherein a few women in a household share numerous husbands... And the head of the household is a woman... and women call the shots... Meanwhile, outside the home, women are treated with far more respect than they are on earth because they are so rare and precious... Obviously, he's not going to get any badges from feminists, but he does at least ask a few interesting questions about the way women were viewed in his own world...The characters explicitly reject using patriotism as a method to revolution.
I think that Prof De La Paz's 'rational anarchism' is also expressed by Jubal Harshaw in 'Stranger', though not in as straightforward a manner. Both seem to say that it's not that hard to figure out what ideal behavior should be but expecting actual live humans to live up that is impossible. After accepting that point, they both want to move on. Yep, humans are hypocritical and sometimes hard to live with. What of it? The other big point of this is that only the direst situation (near term cannibalism here) justifies butting into other people's business. Sadly, this attitude is pretty rare today. The characters explicitly reject using patriotism as a method to revolution. The brain of the book (De La Paz) is an extreme libertarian who has a strong aversion to using the state to make people do anything. There is no attempt to export any kind of ideology to other countries, or even teach some kind of uniform value to its own citizens. How anyone could possibly describe it as 'neo-con' or 'fascist' is beyond me. What's the fascist charge based on? I read a ton of Heinlein in adolescence, and the politics varies a lot book to book. To be honest, extrapolating from the politics in a book to the author's politics is, well, not wholly reliable let's say.
For me, as great as the likes of Arthur C Clarke and Asimov were, they defined the golden age of SF - brilliant, groundbreaking science/concepts but wafer-thin characterisation. Heinlein for me stuck out not only because of his mind-bending concepts but mostly his unique protagonists who - so flawed, so outrageous and out-there (Maureen Johnson from the ‘Cat Who Walks Through Walls’, anyone?) who delivered witty, sarcastic dialogue. This didn't make him necessarily the best for me at the time, just the more humane of SF writers because his ideas seemed less firmly rooted in science than the above mentioned and more on the human condition and the limits of the imagination. I read a lot of his novels when I was a teenager and at the time, felt Heinlein wrote and delivered with a freewheeling sense of irony, certainly arrogance as if he was deliberately going against the grain of SF at the time, wearing his heart on his sleeve and not giving a damn.
And seeing as I’m throwing in my bit about his female characters, anyone remember ‘I Will Fear No Evil’? The dying genius Johann Sebastian Bach Smith who transplants his brain into the body of his secretary, learns how to live like a woman, keeps on having amorous congress left and right, falls in love, and, and, ...; the guys in ‘Starship Troopers’ really wouldn't have approved at all...Have to admit I loved it at the time because it was so different...but then I was only 14...
Heinlein's at his best does great adventure stories that are also full of ideas, and sometimes witty dialogue. When I was a kid, people used to actually say tanstaafl sometimes (geeks obviously, but geeks are people too). His later stuff though, his odd ideas about women get more prominent, his writing flabbier and more self-indulgent, generally he just loses it. But before then, well, he's got a bit dated but he wasn't bad at what he did.
NB: What I always admire about Heinlein is the way he manages to spin a yarn of bullshit so well: you know it's bullshit, he knows it's bullshit but you still swallow it all the same until you've finished the story and then you go "wait a minute..."