Thermochemical equilibrium is one of the most commonly used assumptions in current exoplanet retrievals. As science operations with the James Webb Space Telescope (JWST) draw near and with the planned launch of Ariel, it is crucial to assess the underlying biases and assumptions made when applying self-consistent chemistry to spectral retrievals. Here we use the flexibility of TauREx 3.1 to cross-compare three state-of-the-art chemical equilibrium codes: ACE, FastChem, and GGchem. We simulate JWST spectra for ACE, FastChem, GGchem, and GGchem+condensation containing only the elements C, H, O, and N and spectra for FastChem, GGchem, and GGchem+condensation with a more extensive range of elements, giving seven simulated JWST spectra in total, and then cross-retrieve, giving a total of 56 retrievals. Our analysis demonstrates that, like-for-like, all chemical codes retrieve the correct parameters to within 1% of the truth. However, in retrievals, where the contained elements do not match the truth, parameters such as metallicity deviate by 20% while maintaining extremely low uncertainties <1%, giving false confidence. This point is of major importance for future analyses on JWST and Ariel, highlighting that self-consistent chemical schemes that do not employ the proper assumptions (missing species, fixed elemental ratios, condensation) are at risk of confidently biasing interpretations. Free chemistry retrievals employing parametric descriptions of the chemical profiles can provide alternative unbiased explorations.