In this paper a detailed investigation, based on simulations and experiments of polarized light propagation through textile material, is presented. The fibers in textile material are generally anisotropic with axisymmetric structure. The formalism of anisotropic fiber scattering (AFS) at oblique incidence is first deduced and then, based on this formalism and considered multiscattering, a polarization-dependent Monte Carlo method is employed to simulate the propagation of polarized light in textile material. Taking cotton fiber assemblies as samples, the forward-scattering Mueller matrices are calculated theoretically through the AFS-based simulations and measured experimentally by an improved Mueller matrix polarimeter. Their variations according to sample thickness are discussed primarily. With these matrices polar-decomposed, a further discussion on the optical polarization properties of cotton fiber assemblies (i.e., depolarization $\mathrm{\Delta }$, diattenuation $D$, optical rotation $\psi$ and linear retardance $\delta$) versus the thickness is held. Simultaneously, a meaningful comparison of both the matrices and their polar decomposition, generated from the simulations based on isotropic fiber scattering (IFS), with those simulated based on AFS is made. Results show that the IFS-derived values are strikingly different from those that are AFS-derived due to ignoring the fiber anisotropy. Furthermore, all the AFS-derived results are perfectly consistent with those obtained experimentally, which suggests that the Monte Carlo simulation based on AFS has potential applications for light scattering and propagation in textile material.