Militarist liberal, shaped by his experience in the US Navy during WW2. He’s been accused of thinking of the ideal military officer as a modern warrior-poet.
People who call him an outright fascist are simply wrong, though he meant Starship Troopers seriously. The movie was written and directed as satire, by a director who never finished the very short novel, so don’t consider it as a source of Heinlein’s views.
While he puts military service on a pedestal, the most fascistic element of the work is probably his endorsing of “citizenship through service,” ie you have to earn your vote through a year or whatever of government service. In the movie it’s implied as military only, the book makes it clear you can also do civil service.
That is probably the most common misunderstanding of the novel, even Wikipedia claims it is military only.