<p>Finite difference weighted essentially non-oscillatory (WENO) schemes fill an important need in computational science—in multi-dimensions they can carry out high accuracy simulations at a fraction of the cost of finite volume and discontinuous Galerkin alternatives. Alternative finite difference WENO (AFD-WENO) schemes are variants of WENO schemes which provide the added flexibility of handling structured meshes with complex geometry. AFD-WENO schemes have also been designed recently to handle hyperbolic PDEs with non-conservative products (Balsara et al. in Commun Appl Math Comput, 2024. 10.1007/s42967-024-00374-1), thereby dramatically increasing the range of application areas to which they can be applied. However, one of the deficiencies of higher order WENO schemes stems from the fact that there are stringent problems where the schemes are not Physical Condition Preserving (PCP). This paper rectifies the above-mentioned deficiency by designing and documenting AFD-WENO schemes with a PCP property. The essential idea is to selectively hybridize a low order scheme, which is PCP, with a high order scheme, which may sometimes lose the PCP property. These ideas are packaged into a formulation that works with the fluctuation form for hyperbolic systems, and yet, our formulation is as easy to implement as PCP conditions for conservation laws. The formulation can work seamlessly for conservation laws as well as PDEs with non-conservative products. When the PDE has a conservation form in some limits, the formulation is designed to retrieve that conservation form. We numerically observe that the formulation does not damage the high order accuracy for problems with smooth flow. Several extremely stringent test problems are presented in this paper to illustrate the value of the PCP methods developed here.</p>