  A hybrid C/O/Ne white dwarf (WD) -- an unburned C/O core surrounded by an
O/Ne/Na mantle -- can be formed if the carbon flame is quenched in a super-AGB
(SAGB) star or white dwarf merger remnant. We show that this segregated hybrid
structure becomes unstable to rapid mixing within 2,000 years of the onset of
WD cooling. Carbon burning includes a weak reaction that removes electrons,
resulting in a lower electron-to-baryon ratio ($Y_{\rm e}$) in the regions
processed by carbon burning compared to the unburned C/O core, making the O/Ne
mantle denser than the C/O core as the WD cools. This is unstable to efficient
mixing. We use the results of $\texttt{MESA}$ models with different size C/O
cores to quantify the rate at which the cores mix with the mantle as they cool.
In all cases, we find that the WDs undergo significant core/mantle mixing on
timescales shorter than the time available to grow the WD to the Chandrasekhar
mass ($M_{\rm Ch}$) by accretion. As a result, hybrid WDs that reach $M_{\rm
Ch}$ due to later accretion will have lower central carbon fractions than
assumed thus far. We briefly discuss the implications of these results for the
possibility of Type Ia supernovae from hybrid WDs.
