The evolution of the traditional nuclear magic numbers away from the valley of stability is an active field of research. Experimental efforts focus on providing key spectroscopic information that will shed light into the structure of exotic nuclei and understanding the driving mechanism behind the shell evolution. In this work, we investigate the Z=6 spin-orbit shell gap towards the neutron dripline. To do so, we employed NA(p,2p)CA−1 quasi-free scattering reactions to measure the proton component of the 2₁⁺ state of ^16,18,20C. The experimental findings support the notion of a moderate reduction of the proton 1p_1/2−1p_3/2 spin-orbit splitting, at variance to recent claims for a prevalent Z=6 magic number towards the neutron dripline.