We study the anomalous proximity effect in diffusive normal metal (DN)/unconventional superconductor junctions, where the local density of states (LDOS) in the DN has a zero-energy peak due to the penetration of the odd-frequency spin-triplet $s$-wave pairing. In this study, we consider a two-dimensional unconventional superconductor on the substrate in the presence of a Rashba spin-orbit coupling (RSOC) $lambda$, where the Rashba vector is parallel to the $z$-direction. The anomalous proximity effect, originally predicted in spin-triplet $p$-wave superconductor junctions, is sensitive to the RSOC. It disappears with the increase of $lambda$. On the other hand, the anomalous proximity effect can be switched on by the large $lambda$ values in the spin-singlet $d_{xy}$-wave superconductor junctions. The resulting zero-energy LDOS and the magnitude of the odd-frequency spin-triplet $s$-wave pair amplitude increase with the increase of $lambda$.
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