(I'm sure you know all this; I'm just elaborating for those who haven't sampled the delights of Banks' novels.)
When you can move literally anywhere in the galaxy, amongst virtually any galaxy that hyperspace ships can take you to, there isn't a scarcity of space and machines can create literally anything in this world on demand, so demand is also never a problem.
I think somehow we are misunderstanding eachother, but it makes it much harder to explain this VAST ecosystem when it does appear you might not have even read the series we're all discussing.
Obviously the replacement fertility rate is going to be a lot lower in a society where people can live as long as they please and most choose centuries of life. But the Culture is also vastly wealthier than any real-life low-fertility nation. There's perfect birth control for both sexes and a general absence of destructive impulses among biological Culture citizens (due either to selection pressures or editing). I'd guess that the Minds don't need to nudge much if at all.
Having advanced that argument, I wonder if there is any consistent relationship between material prosperity and fertility. Would a weakly post-scarcity society[2] have higher or lower fertility rates than rich nations do today? There'd be none of the security-in-old-age pressures that drive high fertility in poor nations, but also none of the economic penalties to child rearing that discourage high fertility among the educated middle class in current developed economies.
[1] Ranked by nominal GDP per capita.
[2] A fully robotized productive economy, but we can't just gin up atoms and energy like in the fictional Culture. Also no FTL or teleportation. Real physics only. It's the Silver Plan of post-scarcity, as compared to the Culture's Unobtainium Plan.
The Culture is not limited to biological rates of reproduction. That nobody ever sets off a human forkbomb is a collective choice, somehow.
(Sketchy reply because I'm on a tablet.)