In all the two settings I've seen with some form or matter-matter or energy-matter converters (replicators) they both have either no money system (federation in star trek) or some other form of currency (Days in Strata).
Is this sort of society an inevitable by-product of replicators, are they unrelated or is it not as common as I think?
Such a money-free society assumes unrestricted access to replicator technology, which seems naive. Nation states may restrict access to the technology, as is done in Joe Haldeman's novel Forever Peace, and then wage wars over the technology and the repercussions of it on their economies. This seems completely logical to me; disruptive technologies are outlawed and fought over even today. I expect more draconian bans as technology multiplies the potential force that an individual can command.
Methinks not.
There's always something that can't be replicated, whatever kind of replicators you use. And because of the good old human nature, in the given society, the very same thing will become expensive (in any kind of currency) and people will want to have it.
Consider a few historical examples. Nowadays we take a lot of things for granted, things which would cost a fortune a few centuries ago. Yet we still have a monetary system and social inequalities. The most mundane example I can think of is pepper. I just had a breakfast with the amount of pepper which my great-great-great-grandfather couldn't have earned in years. The fact that it could be produced ad transported almost free of charge compared to a few centuries ago didn't really break the society. Ok, there was the whole thing with the industrial revolution and rise of capitalism and communism, but neither of these made currency obsolete. Not even communism, although in that system money and currency weren't necessarily the same thing. There are many other examples like cheaper energy, faster communication, etc.
The reasons why diamonds and precious metals were always expensive are they couldn't be produced easily as food or other materials. And in Star Trek, there is a substance called Latinum which can't be replicated. Incidentally, the same substance becomes very expensive and pretty much a substitute for money. The fact that the Federation is nominally a moneyless system (and it isn't, they have Federation credits) doesn't mean that there isn't some kind of a currency involved.
Whatever is rare, impossible to easily reproduce and sufficient durable and resistant to elements has the potential to carry intrinsic value and serve the function of money in an economic system.
Also, money doesn't have to have intrinsic value. (Although I would argue that in these cases the real intrinsic value is in its issuer's military strength, but that's a different issue altogether)
