We report a comprehensive small-Angle neutron scattering (SANS) study of magnetic correlations in Mn_1-xFe_xSi at zero magnetic field. To delineate changes of magnetocrystalline anisotropies (MCAs) from effects due to defects and disorder, we recorded complementary susceptibility and high-resolution specific heat data and investigated selected compositions of Mn_1-xCo_xSi. For all systems studied, the helimagnetic transition temperature and magnetic phase diagrams evolve monotonically with composition consistent with literature. The SANS intensity patterns of the spontaneous magnetic order recorded under zero-field cooling, which were systematically tracked over forty angular positions, display strong changes of the directions of the intensity maxima and smeared out intensity distributions as a function of composition. We show that cubic MCAs account for the complex evolution of the SANS patterns, where for increasing x the character of the MCAs shifts from terms that are fourth order to terms that are sixth order in spin-orbit coupling. The magnetic field dependence of the susceptibility and SANS establishes that the helix reorientation as a function of magnetic field for Fe-or Co-doped MnSi is dominated by pinning due to defects and disorder. The presence of well-defined thermodynamic anomalies of the specific heat at the phase boundaries of the skyrmion lattice phase in the doped samples and properties observed in Mn_1-xCo_xSi establishes that the pinning due to defects and disorder remains, however, weak and comparable to the field scale of the helix reorientation. The observation that MCAs, which are sixth order in spin-orbit coupling, play an important role for the spontaneous order in Mn_1-xFe_xSi and Mn_1-xCo_xSi offers a fresh perspective for a wide range of topics in cubic chiral magnets such as the generic magnetic phase diagram, the morphology of topological spin textures, the paramagnetic-to-helical transition, and quantum phase transitions.