I don't know either, I haven't read the Culture books (yet) either so I can't really evaluate that.
I do believe he read a lot of sci-fi in his youth, if only because that would fit the pattern of a young boy who doesn't get along well with their peers and turns towards solitary pursuits like computer programming. He seems exactly the sort to have read lots of Heinlein.
Almost everything about The Culture will be immediately apparent from stuff Musk talks about, but only about half of it would look like he's understood it.
The only real crimes are reading/writing someone's brain without permission (at which point others may call you names and stop inviting you to social events) or destroying a consciousness without backups (where you'll get permanent supervision to make sure you don't do it again). Most biological citizens have a full-brain computer interface for backups and general fun, called a "neural lace".
The AI Minds in charge of everything give themselves fanciful names, which Musk has used for his SpaceX drone ships.
For the reverse:
Almost every biological citizen is gender-fluid, can change physical gender by willing it, and there's a certain expectation that you try things both ways around so you know how to be a good lover. They dislike explosive population growth regardless of if it's organic or machine reproduction, and as everyone can get pregnant if they want to (because everyone can be a woman if they want to and it all works), it's considered quite scandalous to have more than one child.
It's sufficiently post-scarcity that money is considered a sign of poverty. They mostly avoid colonising planets, instead living on ships, or on habitats so large that if one was located at any Earth-Sun Lagrange point (including the one on the far side of the sun), we could see it.