Nobody should take Heinlein's narrators words for granted. He is deservedly famous for being very diverse in presenting the viewpoints of his characters - coming from very different societies.
The moon is a harsh mistress is as much a book about strong friendly AI, as one about alternative ways society could be structured to provide continuity and safety if governments fail to provide. The AI aspect is facinating and much deeper than it seems at first. But if you look closely, there are hints all throughout its quite clever, it just does not care about what its doing, it cares about its friend. It reminds me of the treehouse my neighbours kids once made. The kids tried to make it out of ductape, sticks and plank, and their dad helped them, but also snuck out and nailed a few things and support blocks to make it work.
I ask because when I read it (way back when), I definitely got the impression this was Heinlein speaking in his own voice / his own opinions.
That's exactly what I'm talking about! Read another book, and he'll be speaking his own voice/opinions, to, but they'll be very different.
On books, Heinlein's must read, in my opinion, is "The Moon is the harsh mistress", "Stranger in a strange land" and "Starship troopers", all three being very different. But the one book I would recommend reading first is his lesser known novel, "The door into summer". It is not groundbreaking, but very warm and charming.
I'd recommend The Moon is a Harsh Mistress which is a romp imho, and also happens to be a better insight into his personal politics.
Also, Have Spacesuit Will Travel, Farmer in the Sky, Stranger in a Strange Land and mostly everything by Heinlein, though there was arguably a bit of a drop in quality towards the late end of his career.