The best argument against "Heinlein unironically supports fascism" is the existence of Stranger in a Strange Land, published almost immediately after Starship Troopers. You can't read Stranger and possibly think the author is a full-throated authoritarian. He wrote books that took place in settings, and Troopers took place in a particular setting.

The only probably sincere authorial belief you can really take from it is the linking of full citizenship to some form of civic service. And I'm not sure I disagree completely with that, as a leftist, assuming that service encompasses tasks besides turning foreigners into skeletons. I think there's a bit in there about paraplegics getting citizenship by subjecting themselves to pharmaceutical testing or something. That's civic service.

In fact, one book I read later than others was Job, which is by its premise mostly about adapting to new multiversal realities with different histories and sociopolitical landscapes, While a freak, Heinlein was broadly libertarian and pragmatic. But he did love to explore ideologies through his writing, and they feel more like conversations about the sociopolitical landscape of the setting than endorsements of them.