© ESO, 2015. We study the atomic neutral hydrogen (H I) content of ~1600 galaxies up to z ~ 0.1 using stacking techniques. The observations were carried out with the Westerbork Synthesis Radio Telescope (WSRT) in the area of the SDSS South Galactic Cap (SSGC), where we selected a galaxy sample from the SDSS spectroscopic catalog. Multi-wavelength information is provided by SDSS, NVSS, GALEX, and WISE. We use the collected information to study H I trends with color, star-forming, and active galactic nuclei (AGN) properties. Using near-UV (NUV) -r colors, galaxies are divided into blue cloud, green valley and red sequence galaxies. As expected based on previous observations, we detect H I in green valley objects with lower amounts of H I than blue galaxies, while stacking only produces a 3σ upper limit for red galaxies with MHI<(5 ± 1.5) × 108 and MHI/Lr<0.02 ± 0.006 M/L (averaged over four redshift bins up to z ~ 0.1). We find that the H I content is more dependent on NUV -r color, and less on ionization properties, in the sense that regardless of the presence of an optical AGN (based on optical ionization line diagnostics), green-valley galaxies always show H I, whereas red galaxies only produce an upper limit. This suggests that feedback from optical AGN is not the (main) reason for depleting large-scale gas reservoirs. Low-level radio continuum emission in our galaxies can stem either from star formation, or from AGN. We use the WISE color-color plot to separate these phenomena by dividing the sample into IR late-type and IR early-type galaxies. We find that the radio emission in IR late-type galaxies stems from enhanced star formation, and this group is detected in H I. However, IR early-type galaxies lack any sign of H I gas and star formation activity, suggesting that radio AGN are likely to be the source of radio emission in this population. Future H I surveys will allow for extending our studies to higher redshift, and for testing any possible evolution of the H I content in relation to star-forming and AGN properties up to cosmologically significant distances. Such surveys will provide enough data to test the effect of radio/optical AGN feedback on the H I content at lower, currently rather unexplored H I detection limit (MHI <107).