Multiband and nodal-like superconductivity (SC) with s- + d-wave pairing symmetry have implied that tetragonal iron sulphide (FeS) is a distinctive testbed for exploring unexpected electronic correlations. In particular, the low-moment disordered static magnetism originating from the Fe moment leads to the possibility of the coexistence of magnetic orders (MOs) in the superconducting ground state via the tuning of electronic configurations. Here, guided by density functional theory (DFT) calculations, we found that slightly substitutionally doped chromium (Cr) atoms in tetragonal FeS single crystals can induce both considerable d-orbital reconstruction around the Fermi surface and a local magnetic moment of 2.4 µ_B at each doping site, which could highly modulate the SC ground states of the host. On this basis, a clear magnetic transition and reduced anisotropy of SC were experimentally observed. In particular, SC can survive with a doping content below 0.05. This coexistence of SC and MOs suggests strong spin correlations between Cr dopants and the host through exchange coupling. Further, an electronic temperature-related phase diagram of FeS with Cr doping contents from 0 to 0.07 is also provided. These results demonstrate that the continuous injection of local moments can be a controllable method to use to tune collective orders in unconventional iron-based superconductors.