The era of the James Webb Space Telescope ushers stellar population models into uncharted territories, particularly at the high-redshift frontier. In a companion paper, we apply the Prospector Bayesian framework to jointly infer galaxy redshifts and stellar population properties from broadband photometry as part of the UNCOVER survey. Here we present a comprehensive error budget in spectral energy distribution (SED) modeling. Using a sample selected to have photometric redshifts higher than 9, we quantify the systematic shifts stemming from various model choices in inferred stellar mass, star formation rate (SFR), and age. These choices encompass different timescales for changes in the star formation history (SFH), nonuniversal stellar initial mass functions (IMF), and the inclusion of variable nebular abundances, gas density, and ionizing photon budget. We find that the IMF exerts the strongest influence on the inferred properties: the systematic uncertainties can be as much as 1 dex, 2–5 times larger than the formal reported uncertainties in mass and SFR, and importantly, exceed the scatter seen when using different SED fitting codes. Although the assumptions on the lower end of the IMF induce degeneracy, our findings suggest that a common practice in the literature of assessing uncertainties in SED-fitting processes by comparing multiple codes is substantively underestimating the true systematic uncertainty. Highly stochastic SFHs change the inferred SFH by much larger than the formal uncertainties, and introduce ∼0.8 dex systematics in SFR averaged over a short timescale and ∼0.3 dex systematics in average age. Finally, employing a flexible nebular emission model causes ∼0.2 dex systematic increase in mass and SFR, comparable to the formal uncertainty. This paper constitutes an initial step toward a complete uncertainty estimate in SED modeling.