Symmetric points for (strong) Birkhoff orthogonality in von Neumann algebras with applications to preserver problems

Complete characterizations of left or right symmetric points for (strong) Birkhoff orthogonality in von Neumann algebras and abelian unital C⁎-algebras are given. As an application, we show that every linear strong Birkhoff orthogonality preserver between von Neumann algebras is an algebraic ⁎-isomorphism.