  Under the approximate chiral symmetry restoration, quark interactions with
topological gluon fields in quantum chromodynamics can induce chirality
imbalance and parity violation in local domains. An electric charge separation
({\sc cs}) could be generated along the direction of a strong magnetic field
({\bf B}), a phenomenon called the chiral magnetic effect ({\sc cme}). {\sc cs}
measurements by azimuthal correlators are contaminated by a major background
from elliptic flow anisotropy ($v_2$). Isobaric $^{96}_{44}$Ru+$^{96}_{44}$Ru
and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions have been proposed to identify the
{\sc cme} (expected to differ between the two systems) out of the background
(expected to be almost the same). We show, by using the density-functional
calculated proton and neutron distributions, that these expectations may not
hold as originally anticipated, because the two systems may have sizable
differences in eccentricity and $v_2$ and because their difference in {\bf B}
may suffer from large uncertainties.
