  We prove uniqueness of the essential order for stratified algebras having
simple preserving duality, generalizing a recent result of Coulembier for
quasi-hereditary algebras. We apply this to classify, up to equivalence,
regular integral blocks of $\mathcal{S}$-subcategories in the BGG category
$\mathcal{O}$. We also describe various homological invariants of these blocks.
