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Well it's important to remember that populations decline on earth in developed societies due to specific circumstances. As development increases, education increases, so does knowledge about problems like overpopulation. But moreover, as the society shifts from an industrial to a service based economy, the cost of raising each child goes up and so the best strategy for ensuring your children's success is to have fewer children.
A post-scarcity, interstellar earth civilization would be fantastically more developed, but wouldn't necessarily have any of those other features. The more educated people would understand the value of space colonization as an insurance against extinction, and so the more socially responsible people would have more, rather than less, kids (like it was in the distant past.) And, since they are post scarcity, even though it costs way more to educate each child, that cost means nothing, so there's no incentive to have fewer kids to ensure they get a better chance.
Lastly, in our developed nations in our unusually long period of global peace, the most prestigious jobs are also the safest, whereas the most dangerous jobs are usually held by the lower classes. In UFP it seems that has flipped -- since there is no money, the most valuable thing to people is prestige, and the way people earn prestige is through risk -- i.e. service to humanity, either through colonization, science, exploration in deep space, or defending the Fed in Starfleet. So because humanity is engaging in more high risk endeavours, probably people die a lot more often -- but that also means it is in each parent's best interest to ensure they have the most kids, so even if some of them die (while earning the family prestige for their service) some will survive to pass on DNA.
I think this, if it's the case, really expands that scene where Picard is talking to the rich dude they re-animated from the 20th century, and he is talking down to him because he has a lowly position as a ship's captain. This is hilarious to Picard, not just because of the warm fuzzy statement he gives the guy about life not being about possessions, but because he knows he has one of the most prestigious and sought after roles in his entire society.