We generalize a construction in [BW18] (arXiv:1610.09271) by showing that the tensor product of a based $textbf{U}^{imath}$-module and a based $textbf{U}$-module is a based $textbf{U}^{imath}$-module. This is then used to formulate a Kazhdan-Lusztig
theory for an arbitrary parabolic BGG category $mathcal{O}$ of the ortho-symplectic Lie superalgebras, extending a main result in [BW13] (arXiv:1310.0103).
We establish a Schur type duality between a coideal subalgebra of the quantum group of type A and the Hecke algebra of type B with 2 parameters. We identify the $imath$-canonical basis on the tensor product of the natural representation with Lusztigs
canonical basis of the type B Hecke algebra with unequal parameters associated to a weight function.
