The reference potential of Hg/HgO, SCE will not change, but you will have changes of a diffusion potential. This diffusion potentials occurs at the diaphragma of the reference electrodes and the test solution where you are working in.
The Hg/HgO is very sensitive on that with some hundert millivolts (as OH- and H+ have very different mobilities). With the SCE these diffuison potentials are not very high (some millivolts) because K+ and Cl- have similar mobilities. But in the case that your test solutions has higher concenctration and SCE (that means more than 3 mol/l) you will again have high diffusion potentials.
Therefore one should use Hg/HgO only in electrolytes with the same pH and as the pH of in inner solutions. SCE can be used in solutions with a high pH range (between 1 and 13 without any questions)
If you plan to measure precisely (better than +/- 5mV) you should work with a RHE electrode.