The chiral magnetic effect (CME) is a proposed manifestation of local charge-parity (CP) violation in the strong interaction. Isobaric collisions of (^{96}{44}\mathrm{Ru}+^{96}{44}\mathrm{Ru}) and (^{96}{40}\mathrm{Zr}+^{96}{40}\mathrm{Zr}) at (\sqrt{S_{NN}}=200) GeV were proposed as an effective approach to suppress non-CME backgrounds, since the two systems have the same mass number and were therefore expected to produce similar backgrounds. However, residual differences in nuclear structure and collision geometry can lead to differences in particle production and flow observables between the two isobars, further complicating the identification of a small CME signal. In this work, we investigate the effects of the nuclear structures of Ru and Zr on elliptic flow. We consider two extreme geometric configurations, tip–tip and body–body, to amplify these effects. This comparison provides a direct assessment of how deformation and orientation influence the flow response in the two isobaric systems. Our results demonstrate significant differences in elliptic flow between the two isobars for different configurations, indicating that nuclear structure effects must be carefully considered when interpreting CME measurements in isobar collisions. These findings emphasize the importance of understanding nuclear structure and collision geometry effects, particularly when searching for small CME signals. A detailed study of these deformation effects can help disentangle genuine charge separation associated with the CME from charge separation caused by flow and non-flow backgrounds in the quark-gluon plasma, thereby improving the discrimination between genuine CME signals and background contributions.