  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).
