In most cases it makes enough sense
A serf has a certain amount of crops that didn't get sent to the local lord or get eaten by his family. Easy enough to trade food.
A craftsman could make tools and nails to trade, so that should work out
But a member of a militia? Would he keep a second job on the side and be exempt from taxes due to his service?
As early as the eighth century, the English economy is starting to be monetised. There's a lot of debate on the extent to which the Anglo-Saxon economy was monetised (I recommend Simon Keynes Kings, Currency and Alliances and anything by Rory Naismith), but by the early tenth century, coinage seems to have been pretty widespread, and used in a wide degree of every day transactions as covered by Æthelstan's Grately law codes of 926.
While estates in Anglo-Saxon England often paid their rents in services, goods and food, taxation was monetised, and it's quite likely that somebody like a professional soldier or a craftsman would have been renumerated in coin.