State authority is only truly relevant for collapsing currencies - for a functioning economy and currency, trust and availability are far more important.
Back in medieval and later times, when states were much weaker than they are today, especially economically, and especially small states, people chose which currencies they trusted, and often ignored the coins their local state was minting in favor of other, more trust-worthy coins minted in other places. Those places had no direct power over the people using their currency, and these people were not paying any taxes to them - they were simply choosing a currency they knew was likely to keep its values over the years.
This does happen occasionally in the modern day, with USD-based economies outside the USA, typically in countries with runaway hyper-inflation in their local currency.
Back in medieval and later times, when states were much weaker than they are today, especially economically, and especially small states, people chose which currencies they trusted, and often ignored the coins their local state was minting in favor of other, more trust-worthy coins minted in other places. Those places had no direct power over the people using their currency, and these people were not paying any taxes to them - they were simply choosing a currency they knew was likely to keep its values over the years.
This does happen occasionally in the modern day, with USD-based economies outside the USA, typically in countries with runaway hyper-inflation in their local currency.