We provide accurate assessments of the consequences of violations of self-consistency in Hartree-Fock (HF) based random phase approximation (RPA) calculations of the centroid energy E_cen of isoscalar and isovector giant resonances of multi-polarities L=0-3 in a wide range of nuclei. This is done by carrying out highly accurate HF-RPA calculations neglecting the particle-hole (ph) spin-orbit or Coulomb interaction in the RPA and comparing with the fully self-consistent HF-RPA results. We find

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... at the shifts in the value of E_cen due to self-consistency violation associated with the spin-orbit and Coulomb interactions are comparable or larger than the current experimental errors in E_cen.