Context. The search for twins of the Sun and Earth relies on accurate characterization of stellar and the exoplanetary parameters age, mass, and radius. In the modern era of asteroseismology, parameters of solar-like stars are derived by fitting theoretical models to observational data, which include measurements of their oscillation frequencies, metallicity [Fe/H], and effective temperature T_eff. Furthermore, combining this information with transit data yields the corresponding parameters for their associated exoplanets. Aims. While values of [Fe/H] and T_eff are commonly stated to a precision of ∼0.1 dex and ∼100 K, the impact of systematic errors in their measurement has not been studied in practice within the context of the parameters derived from them. Here we seek to quantify this. Methods. We used the Stellar Parameters in an Instant (SPI) pipeline to estimate the parameters of nearly 100 stars observed by Kepler and Gaia, many of which are confirmed planet hosts. We adjusted the reported spectroscopic measurements of these stars by introducing faux systematic errors and, separately, artificially increasing the reported uncertainties of the measurements, and quantified the differences in the resulting parameters. Results. We find that a systematic error of 0.1 dex in [Fe/H] translates to differences of only 4%, 2%, and 1% on average in the resulting stellar ages, masses, and radii, which are well within their uncertainties (∼11%, 3.5%, 1.4%) as derived by SPI. We also find that increasing the uncertainty of [Fe/H] measurements by 0.1 dex increases the uncertainties of the ages, masses, and radii by only 0.01 Gyr, 0.02 M_⊙, and 0.01 R_⊙, which are again well below their reported uncertainties (∼0.5 Gyr, 0.04 M_⊙, 0.02 R_⊙). The results for T_eff at 100 K are similar. Conclusions. Stellar parameters from SPI are unchanged within uncertainties by errors of up to 0.14 dex or 175 K. They are even more robust to errors in T_eff than the seismic scaling relations. Consequently, the parameters for their exoplanets are also robust.