I'm reading Graeber's book. The origin theory he settles on is that money was created by the state. Kings produced coins, gave them to soldiers, and mandated that the citizens accept the coins as payment for goods. This created a market, and solved the problem of how a kingdom could supply the needs of an army (weapons, clothes, and food).
He does thoroughly deconstruct the barter origin story, by showing that barter economies were actually driven by credit (and thus credit pre-dates money).
The story about religious ceremonies and temples is that in pre-market societies, there was a social currency (wampum, copper rings, special cloths, etc) used for ceremonial purposes. It was when market economies (and market currencies) became entangled with the social currencies that you see the development of slavery.
Given the shadow thrown on Graeber's credibility, I'd say you'll have to treat him similarly to Wikipedia: not a credible primary source. I also found his origin-of-money passages fascinating, but would have to trace those to their sources before I'd believe them.
He does thoroughly deconstruct the barter origin story, by showing that barter economies were actually driven by credit (and thus credit pre-dates money).
The story about religious ceremonies and temples is that in pre-market societies, there was a social currency (wampum, copper rings, special cloths, etc) used for ceremonial purposes. It was when market economies (and market currencies) became entangled with the social currencies that you see the development of slavery.