  From core to atmosphere, the oxidation states of elements in a planet shape
its character. Oxygen fugacity (fO$_2$) is one parameter indicating these
likely oxidation states. The ongoing search for atmospheres on rocky exoplanets
benefits from understanding the plausible variety of their compositions, which
depends strongly on their oxidation states -- and if derived from interior
outgassing, on the fO$_2$ at the top of their silicate mantles. This fO$_2$
must vary across compositionally-diverse exoplanets, but for a given planet its
value is unconstrained insofar as it depends on how iron (the dominant
multivalent element) is partitioned between its 2+ and 3+ oxidation states.
Here we focus on another factor influencing how oxidising a mantle is -- a
factor modulating fO$_2$ even at fixed Fe$^{3+}$/Fe$^{2+}$ -- the planet's
mineralogy. Only certain minerals (e.g., pyroxenes) incorporate Fe$^{3+}$.
Having such minerals in smaller mantle proportions concentrates Fe$^{3+}$,
increasing fO$_2$. Mineral proportions change within planets according to
pressure, and between planets according to bulk composition. Constrained by
observed host star refractory abundances, we calculate a minimum fO$_2$
variability across exoplanet mantles, of at least two orders of magnitude, due
to mineralogy alone. This variability is enough to alter by a hundredfold the
mixing ratio of SO$_2$ directly outgassed from these mantles. We further
predict that planets orbiting high-Mg/Si stars are more likely to outgas
detectable amounts of SO$_2$ and H$_2$O; and for low-Mg/Si stars, detectable
CH$_4$, all else equal. Even absent predictions of Fe$^{3+}$ budgets, general
insights can be obtained into how oxidising an exoplanet's mantle is.
