Etingof's conjecture on restriction of unitary representations

Let $W$ be a type $B$ complex reflection group, let $\mathcal{O}_c(W)$ be its rational Cherednik algebra category $\mathcal{O}$ at parameter $c$, and let $W'\subset W$ be a parabolic subgroup. For an irreducible representation $L$ in $\mathcal{O}_c(W)$, denote by ${^\mathcal{O}\operatorname{Res}}^W_{W'}L$ its parabolic restriction. Etingof's conjecture. If $L$ is unitary, then

$${^\mathcal{O}\operatorname{Res}}^W_{W'}L$$

is unitary. This conjecture concerns the preservation of unitarity under parabolic restriction; the supplied text does not state whether it has been proved or disproved.