I'm not sure exactly what cashless is, but I do have an answer. Just because something isn't printed or in coin form doesn't mean there isn't a medium for exchanging goods and services. In STU you don't have to trade a chicken for a head of lettuce.
Currency is still alive and well, sort of. Clearly Roddenberry wanted it gone. So let's start with there's no currency.
Ronald D. Moore commented: "By the time I joined TNG, Gene had decreed
that money most emphatically did NOT exist in the Federation, nor did
'credits' and that was that. Personally, I've always felt this was a
bunch of hooey, but it was one of the rules and that's that." (AOL
As Moore commented, it's a bunch of hooey. How do people get the things they need? How is it decided who gets the biggest house, apartment, etc. Who gets the oceanside view? Can a person just travel around for free, stay where they want, eat what they want, never work, etc? It makes no sense.
Roberto Orci and Alex Kurtzman, screenwriters of Star Trek, said in a
question-and-answer session with fans that "there's money, or some
kind of credit system" in the alternate reality.
So you see more screenwriters above stating that there's something but don't want to contradict Roddenberry's ideal dream.
Below are examples to in various shows to show that there's some form of currency.
Kirk said to Picard: "This is my house, I sold it years ago." inside
the Nexus, referring directly to the sale of his former home. (Star
If Kirk sold his house there must have been some form of currency, credit, or something.
When preparing to fight the Klingons on Organia, Kirk said "Well, the
Federation has spent a lot of money on our training..." (TOS: "Errand
Above could be just a manner of speech, but it also could be referring to resources, credits, something like money.
Cyrano Jones told Lieutenant Nyota Uhura that "a tribble is the only
love that money can buy." (TOS: "The Trouble with Tribbles")
As I recall he sold Tribbles to Federation officers so they must have had some form of currency to pay him.
If your only question is whether a member planet has to give up currency, clearly that is not the case, read below. (But I think your question is more than that)
The Bank of Bolias was a major financial institution. Bolarus IX is a
Federation member planet, that apparently has a market economy. (DS9:
"Starship Down", "Who Mourns for Morn?")
Above is an actual Federation member that clearly has a financial institution and some sort of market economy.
SISKO: I remember, Jake, I wasn't much older than you when I left for
San Francisco to go to Starfleet Academy. For the first few days, I
was so homesick that I'd go back to my house in New Orleans every
night for dinner. I'd materialise in my living room at six thirty
every night and take my seat at the table just like I had come down
JAKE: You must have used up a month's worth of transporter
I just watched this episode. It was clear from the episode that Sisko was speaking of actual credits of some sort.
In 2373, Quark indirectly caused damage to a cargo bay. Quark was
informed that he would have to bear the cost burden for the repairs.
(DS9: "Business as Usual")
So there's a cost involved. They also charged rent on the station, although I'm not sure if that went to the Federation or Bajor.
On numerous occasions, Starfleet officers have gambled to win latinum at Quark's Bar, including Julian Bashir, William Riker, Jadzia Dax.
DS9 "The Darkness and The Light":
DAX: I didn't lose that much.
WORF: Two bars of latinum. I hope you have it.
DAX: I have it. Most of it. Worf?
DAX: Fine. I'll borrow it from Quark. He likes me.
WORF: Major Kira's friend is ready for transport. Quark may lend you
the money, but remember Rule of Acquisition number one hundred and
eleven. Treat people in your debt like family, exploit them.
DAX: You know the Rules of Acquisition?
WORF: I am a graduate of Starfleet Academy. I know many things.
So we see from the above dialogue several things. One the art of betting is alive and well in the Federation. Two is that Starfleet officers understand the concept of money. The third thing is that both Dax and Worf keep currency around and have a way of acquiring it. Fourth and final is that it can be inferred from Worfs last comment that Starfleet Academy actually teaches the Rules of Acquisition or at least some class is offered that explains that concept.
On Voyager they start using Replicator Rations as a form of currency.
And of course the Picard family vineyards and wine making business. Does his brother give away the wine for free? How does he get the land and the equipment to have vineyards and make wine?
So the answer I believe is that Roddenberry didn't want currency, credit, or any of that stuff around, he had this ideal universe he wanted. But...his writers believed that was impossible to do. They couldn't go against him directly. There's clearly examples and allusions to various forms of currency and credits in the Star Trek Universe. So that's your answer I believe.