There was no population change. The majority stayed christian and communities were not expelled. The islamic way of doing sound money trade took over many parts of the world that way.
Discussion
Yes, by rule of a different society. Question was when "a society switched from a fiat standard to a hard or sound money standard" the last time. The intention behind a this question was to find out, if a people has ever become reasonable on its own and switched back to sound money, without being conquered or dominated by another culture. And behind that lies the question of how likely it is that we in the West will ever experience a Bitcoin standard.
What i am trying to say: When societies accepted new rulers it often reflected their preference for systems offering more stability, freedom, and prosperity. Societies embraced islamic rule (and kept their own language and religion for centuries) for its ability to give rhem a better life.
While the religious aspect of Islamic expansion is often emphasized, the technical aspects are neglected. Islam was not solely a religious phenomenon but also a socio-economic transformation driven by practical benefits.
Regarding the question of whether "people become reasonable on their own," I believe that external catalysts are almost always necessary to inspire change and shift attitudes. Societies that remain closed off and resistant to outside influences are often the first to stagnate and decay.