I watched the episode again, and I picked up on something that I missed.
In all of the Star Trek series physical money has always been something that's not been used in the Federation. You get hints that there is still some form of money still in use, probably for cultures that haven't moved past it. I THINK money is mentioned/used in ST:TOS "A Piece of the Action," which makes sense given that that planet is emulating the 1920s.
In this episode of the Orville they talk about why money is obsolete... matter synthesis technology. Essentially, if you can synthesize pretty much everything you need at the push of a button, you don't need cash to buy things, and reputation is the new "currency."