Good question.
Sometimes I think it's just "what if?". I read that he tried to make all kinds of taboo subjects acceptable, or at least constructed circumstances where they would be. For example in Stranger in a Strange Land it was cannibalism. His views, as reflected in his books, did change over the years. He was Libertarian rather than conservative certainly, and his characters obeyed rules as and when they wanted to.
Something I noticed throughout was that he seemed to have an obsession with reproduction, rather than sex. I'm currently rereading The Number of the Beast (a weird story where he introduces a concept where fiction becomes fact in other dimensions, which enables him to allow his characters from other books to meet). Anyway, two couples get married in the first few pages and immediately both women are pregnant. I have a personal theory that it's connected to the fact Heinlein himself never had any children.
Heinlein was a graduate of Annapolis with training in engineering. A lot of his fiction, as has been pointed out here by others, supported his opinion that service in the military was a valid and honorable career choice.
In some ways, I see Stranger in a Strange Land following Starship Troopers as a statement of "you don't know me" from Heinlein to those that labeled him militaristic and fascist as a result of the latter work. He did seem to tend to explore taboo subjects and sometimes in odd ways.
I think he was pretty liberal until just after WWII and then did an about face to some degree with strong libertarian influences.
I've been reading Heinlein's work since I was about 8. My father and mother had a couple of his novels in our home library that got me started off. He was from Missouri too.
I like David Brin as well. That was a good article.
It seems I have a fancy for hard science, science fiction authors, though not exclusively.