Emission line diagnostic diagrams probing the ionization sources in galaxies, such as the Baldwin-Phillips-Terlevich (BPT) diagram, have been used extensively to distinguish active galactic nuclei (AGN) from purely star-forming galaxies. However, they remain poorly understood at higher redshifts. We shed light on this issue with an empirical approach based on a z 0 reference sample built from 00,000 Sloan Digital Sky Survey galaxies, from which we mimic selection effects due to typical emission line detection limits at higher redshift. We combine this low-redshift reference sample with a simple prescription for luminosity evolution of the global galaxy population to predict the loci of high-redshift galaxies on the BPT and Mass-Excitation (MEx) diagnostic diagrams. The predicted bivariate distributions agree remarkably well with direct observations of galaxies out to z 1.5, including the observed stellar mass-metallicity (MZ) relation evolution. As a result, we infer that high-redshift star-forming galaxies are consistent with having normal interstellar medium (ISM) properties out to z 1.5, after accounting for selection effects and line luminosity evolution. Namely, their optical line ratios and gas-phase metallicities are comparable to that of low-redshift galaxies with equivalent emission-line luminosities. In contrast, AGN narrow-line regions may show a shift toward lower metallicities at higher redshift. While a physical evolution of the ISM conditions is not ruled out for purely star-forming galaxies and may be more important starting at z ≳ 2, we find that reliably quantifying this evolution is hindered by selections effects. The recipes provided here may serve as a basis for future studies toward this goal. Code to predict the loci of galaxies on the BPT and MEx diagnostic diagrams and the MZ relation as a function of emission line luminosity limits is made publicly available.