The entropicity conjecture for idempotent algebras with the generalized entropic property

Let $(A,f)$ be an idempotent algebra with the generalized entropic property.

Entropicity conjecture. Every idempotent algebra $(A,f)$ with the generalized entropic property is entropic.

The paper has already exhibited finite non-entropic idempotent algebras satisfying the generalized entropic property, so the conjecture is contradicted by the examples discussed there.