It's great to see Heinlein here! I've never read anything by him, so this was my first exposure. I've been meaning to remedy that, so I have a copy of "The Moon is a Harsh Mistress" on my shelf but haven't gotten to it yet.
Interesting story, though time paradoxes tend to get under my skin. At least in this case it was entirely intentional and had lanterns hung all over it, which is much better than just an accidental.
I expect this was very controversial in its day with the transgender character, which is cool in and of itself. Is it possible for one person to be fertile with both her male and female sex organs? I guess I don't know enough about hermaphrodites to know for sure, but it seemed unlikely.
What got under my skin more than the time paradox was the genetics. Mating through inbreeding is more likely to cause birth defects, yes? So the moment he had a baby, every version of him would meet infinite potential for birth defects in the human genome, due to his infinite unbranching family tree. And what of the genetic mutations that over many generations lead to evolution? Why does he end up being the same person with each iteration?
Interesting that what appears to be a fairly well-rounded cast of 4 is all just a cast of one with the same guy in different guises. That alone makes the story worth a listen.
I don't really like the title, though, just based on digressive philosophy that has nothing to do with the rest of the story. I like a title that foreshadows the actual story.
For those who mentioned disliking the Whore Corps, and I agree with you, that was a pretty common trope back in the 50s. At a library liquidation sale last year I bought a "Best of F&SF" book which anthologized a bunch of stories that ran in F&SF in its early years. Most of them were just downright terrible, whether because of their datedness or just bad writing, these days. One was particularly good called Gorilla Suit that I'd highly recommend as humor reading for anyone who can find it. Anyway, there was a story in there, by, I think, C.S. Lewis which was centered around a similar Whore Corps. The assumption seemed to be that it made sense for only men to be astronauts and women would only be worthy for space travel as sexual entertainment. Which goes to show how views of gender have changed over the years, yes? Anyway, as if the basic premise of the Lewis story weren't offensive enough to current views, the women who end up being sent up there were all "undesirable" by the astronauts, one being very old and thin as a rail and the other being overweight. And that was really the whole point and plot of the story, how annoying these women were. All You Zombies at least did not make that the entire point, it used it as part of the setting.