The dependence of the single-particle strength on the difference between proton and neutron separation energies is studied for oxygen isotopes in a wide range of isospins. The cross sections of the quasi-free (p, 2p) reaction on 14,16,18,22,24O were measured at intermediate energies. The measured cross sections are compared to predictions based on the distorted wave impulse approximation and shell-model psd valence-space spectroscopic factors. The reduction factors, which are the ratio of the experimental cross sections to the theoretical predictions, show no apparent dependence on the proton–neutron separation energy difference. The result is compatible with the result of the (e, ep) reaction on stable targets and with the predictions of recent ab initio calculations.