Did you misinterpret Starship Troopers to be straight endorsement of militant fascism?

yes!

There's your problem. Just because an author writes a book with a world building premise does not mean they fully endorse the world created. In Stranger in a Strange Land, which came out less than two years later, the main character creates a free love hippie movement. The Moon is a Harsh Mistress, a few years later, is about a revolution against authoritarian oppression.

If a person names as his three favorites of my books Stranger, Harsh Mistress, and Starship Troopers … then I believe that he has grokked what I meant. But if he likes one—but not the other two—I am certain that he has misunderstood me, he has picked out points—and misunderstood what he picked. If he picks 2 of 3, then there is hope, 1 of 3—no hope. All three books are on one subject: Freedom and Self-Responsibility.

Heinlein wrote thought experiments. He wrote about the relationship between people and the society they live in. To that end, he wrote about a number of different kinds of society, and how people related to them. Insofar as you could ascribe any particular political ideology to him based on his writings, he was broadly anti-authoritarian. Nothing remotely close to a Nazi.