We have investigated the cluster isolated desynchronization, a symmetry-breaking state, in the delay-coupled vertical-cavity surface-emitting lasers (VCSELs) networks subject to variable-polarization optical feedback (VPOF). It is shown that, in the VPOF-VCSELs networks, the elusive isolated desynchronization phenomenon could emerge out of the cluster synchronization by the common-signal injection approach from an additional auxiliary VCSEL. The influences of parameters in VPOF-VCSELs networks on the existence and stability of isolated desynchronization are systematically investigated. Moreover, the generality of the proposed scheme is validated in the VPOF-VCSELs network with real-world network topology (Nepal power grid network). Our results offer a new insight to manage the synchronization patterns of a VCSELs network.