We compared the X-ray polarization properties in the 1–100 keV band of homogenous static equatorial obscuring media around accreting compact objects. We performed simulations of partially ionized and partially transparent 3D toroidal structures with the STOKES code (Goosmann & Gaskell 2007; Marin et al. 2012b, 2015; Marin 2018), which is an MC simulation suitable for studying the effects of scattering and absorption. Placing the source of low (up to a few %) polarized source of isotropic power-law emission in the center of the axially symmetric equatorial obscurer, we defined distinct geometries for the reprocessing studies: the wedge-shaped torus and elliptical tori with various eccentricities. When avoiding the observed polarization state of spectral lines by selecting the 3.5–6 keV and 30–60 keV bands, we found large dependence of the polarization fraction on inclination, half-opening angle, density of the scatterer and ionization level. We found relatively minor impact (up to a few %) of primary polarization state and moderate impact of the primary power-law index Γ (low tens of % in very specific geometries). Overall, the diversity in resulting polarization is striking. The polarization fraction can vary from completely unpolarized results up to high tens of %, with large degeneracies with respect to the geometries examined and the density and ionization effects. The resulting polarization angle can be either perpendicular or parallel with respect to the main axis of symmetry, as we do not take into account any general-relativistic effects. The former scenario is favoured for low half-opening angles, high column densities, high ionization levels and low inclinations. The opposite configurations will more likely result in a parallelly oriented polarization angle, while the intermediate cases depend on subtle details of relative size, shape and composition of the obscurer. The X-ray polarization fraction typically reaches a maximum for moderate inclinations per given half-opening angle, effectively providing 2 solutions as a diagnostic tool for energy-integrated observations. The modelling results are roughly consistent with other codes in the literature (Ghisellini et al. 1994; Ratheesh et al. 2021; Ursini et al. 2023; Veledina et al. 2023) and STOKES code computations performed for more specific configurations (Goosmann & Matt 2011). We obtained similar geometry effects of the equatorial obscurers on polarization studied in the optical and UV wavelengths (Kartje 1995; Goosmann & Gaskell 2007), confirming the fundamental geometrical explanations provided therein. In addition, we provided a different perspective and usage example of the MC simulations by studying in detail the equatorial obscuration in the context of recent IXPE observation of the XRB Cygnus X-3 (Veledina et al. 2023). Focusing on the IXPE operational band 2–8 keV, we showed maps of predicted polarization state with respect to inclination, half-opening angle, different toroidal geometries, equatorial column densities and ionization levels for singlescattered photons and all photons (including direct radiation). For constant density, ionization level and geometrical parameters, the actual chemical composition seems to have low effect, if one does not have ambitions to study the polarization signatures in spectral lines in detail. In the continuum 3.5–6 keV band we obtained a match between the moderate and high density full MC simulations with the single-scattering option and the analytical single-scattering results presented in Veledina et al. (2023). The parameters of the primary radiation are possible to explore through type-1 viewing angles, although the impact of equatorial reprocessing is present, resulting in change of polarization up to ∼ 1% from the initial state. For type-2 viewing angles the primary state of emission is washed out up to ∼ 10◦ of error in inclination and Θ, which is negligible compared to the effects of changing density and ionization. Although spectroscopy and polarimetry in other wavelengths can significantly help to lift the model degeneracies, X-ray polarimetry can do so already, if energy-dependent polarization is obtained with sufficient photon statistics in the 2–8 keV band, which is particularly sensitive to partial transparency effects and spectral lines. This was also illustrated on the recent IXPE observation of the obscured accreting stellar-mass black hole in Cygnus X-3 in comparison with the MC models within the limits of unavoidable numerical noise for reasonable computational times.