Quantum critical points (QCPs), zero-temperature phase transitions, are windows to fundamental quantum-mechanical phenomena associated with universal behaviour. Magnetic QCPs have been extensively investigated in the vicinity of antiferromagnetic order. However, QCPs are rare in metallic ferromagnets due to the coupling of the order parameter to electronic soft modes. Recently, antisymmetric spin-orbit coupling in noncentrosymmetric systems was suggested to protect ferromagnetic QCPs. Nonetheless, multiple centrosymmetric materials host FM QCPs, suggesting a more general mechanism behind their protection. In this context, CeSi_2-δ, a dense Kondo lattice crystallising in a centrosymmetric structure, exhibits ferromagnetic order when Si is replaced with Ag. We report that the Ag-substitution to CeSi_1.97 linearly suppresses the ferromagnetic order towards a QCP, accompanied by concurrent strange-metal behaviour. Herein, we suggest that, despite the centrosymmetric structure, spin-orbit coupling arising from the local noncentrosymmetric structure, in combination with nonsymmorphic symmetry, can protect ferromagnetic QCPs. Our findings offer a general guideline for discovering new ferromagnetic QCPs and highlight one new family of materials within which the interplay of topology and quantum phase transitions can be investigated in the context of strongly correlated systems.