What reionized the universe? What are the masses, star formation rates, and formation histories of galaxies in the early universe? Answering these questions requires a detailed understanding of the nebular emission properties in galaxies. However, the complex physics governing nebular emission in galaxies, particularly in the early universe, often defy simple low-dimensional models. We present Cue, a highly flexible tool for interpreting nebular emission across a wide range of abundances and ionizing conditions of galaxies at different redshifts. Unlike typical nebular models used to interpret extragalactic nebular emission, our model does not require a specific ionizing spectrum as a source, instead approximating the ionizing spectrum with a 4-part piece-wise power-law, along with freedom in C/O, N/O, O/H, electron density, and total ionizing photon budget. This flexibility allows us to either marginalize over or directly measure the incident ionizing radiation, thereby directly interrogating the source of the ionizing photons in distant galaxies via their nebular emission. We demonstrate the use of Cue on a variety of simulated and real JWST data. For example, Cue reproduces the emission lines and ionizing production efficiency of GS-NDG-9422, a peculiar z = 6 galaxy with a claimed top-heavy IMF, with an more orthodox ionizing continuum consistent with a combination of normal low-metallicity stellar populations and a low-luminosity AGN. Additionally, we show the inferences of Cue applied to JWST/NIRSpec spectroscopy of z ∼ 2 galaxies (PI: Belli, ID 1810), specifically identifying the dominant ionizing sources in normal galaxies at the cosmic noon.