No money in the future was something established from the mouth of James Kirk in The Voyage Home, which was released in 1986, almost a year before TNG first aired in 1987.
The precise dialog was:
McCOY: It's a miracle these people ever got out of the twentieth century.
KIRK: They're still using money. We've got to find some.
As Gillian and Kirk leave the restaurant:
GILLIAN: Uh, ...could we have that to go, please?
WAITER: Sure! Who gets the bad news?
GILLIAN: Don't' tell me they don't use money in the twenty-third century.
KIRK: Well, they don't.
So that is what has to be interpreted. Note that this is less than two decades after money was often mentioned in TOS and TAS.
Kirk's words could be interpreted as meaning that 20th century Earth still uses coins, paper money, and credit cards, while the 23rd century uses some form of electronic money transactions.
Perhaps the true money less society didn't appear until the era of Picard.