I think you've got it backwards.
Diversity implies different forms of order, not disorder.
Homogeneity implies disorder.
A shuffled deck of cards is more homogeneous and disordered than a stacked deck.
When things flow across a gradient, like heat or matter flow, to reach a state of equilibrium or homogeneity, entropy is increased. This is a natural driving force.
Entropy increases as things become the same everywhere.
So in your peculiar application of entropy to civilization, entropy increases as cultural diversity decrease.