Worf lived on Gault for a while, and it described it as a farming colony (“Heart of Glory”; “Let He Who is without sin”). Plus we also had Omicron Ceti III (“This Side of Paradise”) that was set up as a farming colony. So not everything was synthesized.Robert may not have had a replicator... But he sure as ###k had a food synthesizer, which had been around conceivably since 200 years before he started making children, so it was his great grandfathers decision to modernize that much.
If they were also holding out on a synthesizer, that means that they were the weirdo family who was a burden on every one else, since the economy had to bend to keep the Picards alive, as 2 thousand pounds of food per person had to be grown the old fashion way, as well as maybe birthing a limited number of animals for slaughter.
That barely makes sense.
The United Earth probably lied to the Picards.
"Here's a truck load of unsynthesized food, yes, that's right completely unsynthesized food, totally real, it's real food, would I lie to you?"
Similar to how antivaxers should be given free milk by the state.
Special, special, magic milk, that is not full of vaxinated goodness, would i lie to you?
Robert owned a farm.
Maybe he did grow all his own food?
But you also have to wonder how there were no revolts if everyone was forced to eat resequenced protein, or as Kirk said in “Charlie X” ‘meatloaf that looks like turkey’.