We designed a metasurface made of a monolayer of spherical nanoparticles embedded in a dielectric slab, which exhibits transmission properties independent of the incidence angle. Adjusting the electromagnetic coupling between high-index dielectric and hybrid core-shell nanoparticles enables the metasurface to operate in low-pass, bandpass, as well as band-stop regimes in the visible and near-infrared spectral ranges. We demonstrate how symmetric properties of spherical nanoparticles determine the response of the metasurface, resulting in a spectral filter with a wide angular acceptance range. We study transmission characteristics of the metasurface, such as frequency selectivity, the slope of filtering at cutoff frequencies, and the robustness of the metasurface against experimental variations in geometrical parameters. Our analyses show that the proposed approach can be used to design angular-independent spectral filters with the same material platform and approach to operate in different regimes and spectral ranges.