Rivest--Vuillemin's generalized Aanderaa--Rosenberg conjecture

Let $E$ be a finite ground set, let $\mathcal{F}\subseteq 2^E$ be a set system, and let $G\subseteq \operatorname{Symm}_E$ be a symmetry group acting transitively on $E$. Assume that the empty set belongs to $\mathcal{F}$ while the full set does not. Rivest--Vuillemin's conjecture. Under these assumptions, $\mathcal{F}$ is evasive.

This conjecture is a symmetry-based generalization of evasiveness questions for graph properties. The excerpt provides the formulation but no proof or status evidence, so its resolution is left open.