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Monolayer SnS2 has emerged as a promising visible-light photocatalyst for photoelectrochemical applications, owing to its strong optical absorption in the visible range and excellent chemical stability. Despite its reduced dimensionality - where excitonic effects are expected to be pronounced - comprehensive theoretical investigations of bound excitons in this material remain scarce. Notably, unlike most two-dimensional hexagonal crystals, monolayer SnS2 exhibits its lowest single-particle transition at the M point of the Brillouin zone (BZ). Here, the electronic valence bands form a saddle point while conduction states display a minimum with pronounced anisotropy, creating a distinctive band topology whose impact on optical excitations has not yet been systematically explored. In this work, we present a first-principles study of bound excitons in monolayer SnS2 based on state-of-the-art many-body perturbation theory, employing the GW approximation and the Bethe-Salpeter equation (BSE). We analyze how band symmetry and anisotropy shape the excitonic wavefunctions and transition dipole moments. By resolving the exciton dipoles in momentum space for different linear light polarizations, we demonstrate that linearly polarized light lifts the C3 rotational symmetry relating the three inequivalent M points, giving rise to three linearly independent excitonic states. This polarization-selective coupling, previously identified for saddle points in graphene, is achieved in SnS2 for bound excitons and provides a potential route toward state encoding schemes in valleytronics applications.